ACE Class 9 Maths LIVE | CBSE | Perimeter & Area + Introduction to Probability | NCERT

[00:00:04]Hello everyone. Class 9th champions.

[00:00:07]Class 9th ninjas. My dear lovely kids.

[00:00:09]Hi everyone. My lovely lovely lovely hello to all my champions. So I know you must have been waiting for me for last few days. So let's join quickly champions and please let me know first.

[00:00:21]Am I audible to you all? Am I clearly visible? Am I audible to you all? Please let me know first. And this session is going to be powerful because I'm going to complete two new chapters of your ganit mji the chapter number six measuring space parameter and area and one more chapter chapter number seven that is probability. Okay. So before I start this session this fabulous session please join quickly everyone and let me know am I audible to you all you all can hear me you all can see me I am visible to you all. So this session is going to be very important for you all. Class n champions I really apologize uh due to I mean few problem due to uh little occupancy you know team could not schedule the live before and that's why I know you might not be aware of the live because life is just scheduled uh right away before 2 to 3 minutes I know so I really really apologize sorry my dear champions so please join everyone quickly class 9th ninjas Yes sir. Audible and visible. Hi Fern.

[00:01:30]Hi. How are you Fern? All okay. All good. So I'm going to teach you champion chapter number six measuring space parameter area and chapter number seven probability. And as you all know my method what I used to do in every chapter I used to teach from basics from zero to hero from basics to advanc. This is my teaching method. Okay.

[00:01:54]So please join everyone quickly. So let's begin with chapter number six.

[00:01:58]Measuring space and parimeter area.

[00:02:00]Okay. So moving to the first question here. Look at the first question. Find the parameter. And these questions are from your Ganit MJI textbook by the way.

[00:02:08]Please let me know everyone. I hope you you all have Ganit MJI and you must have been solving your Ganit MJI in your school as well as at your at your home in self studies. Okay. So question number one is find the parimeter of a rectangle whose length is 12 cm and breadth is 8 cm. This is very easy question. First time watching your session. Wow great fage. Welcome welcome welcome. If you are I mean first time on this channel I hope you must have subscribed the channel for the future notification and if you're in class 9th or in 10th this channel is best for you.

[00:02:45]Trust me. Okay. So if you if you haven't subscribed the channel yet, go and hit the subscribe button first. Okay. So first question is find the parimeter. Do you know parimeter means what? Parameter means total boundary length anything whether it is a rectangle, a square, circle whatever the total boundary length outer boundary length is called parimeter. So if we talk about a rectangle, this is rectangle we have and this is length and this is breadth. And if this is length, it has to be length.

[00:03:19]If this is breadth, it has to be breadth. And what will be the parimeter?

[00:03:23]I have already told you champion the parimeter means boundary. Boundary length. So parameter of rectangle will be boundary length. Sum of all these boundaries. Sum of all these boundaries. So L + B + L + B. So both are coming two times. L is 2, B is 2. So we can take two common. So the formula will look like 2 into L + B. This is the formula for parameter of rectangle. Now in this question, length is given to you 12 cm and breadth is given to you 8 cm. Now we can put the values here. So 2 into length we have 12 + 8. So 2 into 20 and this will be 40 cm. The parimeter always comes in centimeter or meter. But area goes in square, centime square, meter square. If we are calculating area, area will go in square form. Cime square. If the dimensions are in meter, me square will be there. But for parimeter only cm or only meter will be there. This is the difference. Clear? Yes. Very good.

[00:04:30]Moving ahead. The parimeter of the square field is 64 m. Okay. Okay. Read the question from here till here. Read the first line. So according to the first line, the parimeter of a square is already given to you. Here in this question, parimeter of square which is already given to you. You read the first line carefully. So this is 64 m. Right? Find the length of each of the side. We all know the property of square. In a square all the sides are equal to each other. This is the property of square. All the sides are equal to each other. So what will be the parimeter? Parimeter will be L + L + L + L. So this is called 4 into L. 4 into side. Now in this question parimeter is already given to you. Now we can put here 64 and equal to 4 into L. So what will be L here? L will be four is in multiply. When four will come this side.

[00:05:30]So it will look like 64 divided by 4 and we have 16. So L is equal to 16 cm. So the side of square is equal to 16 cm.

[00:05:40]Clear everyone sir this is new NCRT. Yes FASA this is new NCRT. So in this question perimeter was already given to you and the question is asking find the length of the square. So we have parimeter formula parameter is equal to 4 into length mean 4 into side. You guys can memorize this formula.

[00:06:00]In this form parimeter is equal to 4 into side. This is the parimeter of square.

[00:06:06]Yes. Yes. Yes. This is the parimeter of square. 4 into side. And now in this question parimeter was already given to you. Okay. Moving ahead. Third question.

[00:06:14]Look at the third question. Find the area of a rectangle rectangular garden.

[00:06:20]Okay. Okay. So there is a rectangular garden. This is the rectangular garden whose length is 25 cm. Okay. Okay.

[00:06:28]length is 25 m and breadth is 15 m and we have to find out area.

[00:06:36]So my dear champion area of rectangle area of rectangle is what?

[00:06:45]Length into breadth. Length into breadth. This is the formula length into breadth. And length is given to you directly. Length we have is 25 and breadth we have is 15. Now could you please multiply 25 into 15? So if you multiply 25 into 15 25 into 5 will be 125 and 25.

[00:07:06]So we have 5 7 and this is three. So we have 375 and my dear champion we all are calculating square. So in square the answer will always go in square. If the dimension is in meter so answer will go in me square. If the dimensions are in centimeter, answer will go centime square. So this is the formula. Yes.

[00:07:28]Clear everyone.

[00:07:30]Hi s you guys are talking with each other. Wow.

[00:07:36]Mafia. Mafia is also in your chat. Oh my god. I'm little scared. Okay. So I hope this is clear to you all. Area of rectangle. The formula we have is length into breadth. This formula champion.

[00:07:48]Please don't forget the formula. For formula is very important. Moving ahead.

[00:07:52]Look at the next question. Okay. A wire of length 44 cm. Please read the question carefully. Don't be so curious to get the answer directly. No. First read the question. Have patience. Stay calm. Understand the language.

[00:08:08]Understand the story given there. Then try to recall the formula which formula we should use there. Okay. Okay. So a wire of length. So we have a wire. Let's say this is a wire and the length of wire is 44 cm.

[00:08:23]Say cm 44. This is cm. Okay. 44 cm. This is the total length of the wire. 44 cm.

[00:08:31]Okay. Is bent is bent. Bent turning bent to form a square. Okay. Okay. So we are making a square from this wire. Same wire is there. And we have converted this wire in the shape of square. And we all know the side of square is equal to each other. All the sides are equal to each other. L L.

[00:08:55]And do you know this straight wire has bent in the form of square. So the total length of the wire will be equal to the total length of the boundary because the same wire was you know changed the wire same wire was reshaped in the form of square. So the length of that wire and the length of boundary of this square will be equal to each other. So we can write here L + L + L + L and that is equal to 4 L 4 into L will be equal to 44. Right? So L will be equal to 44 / 4 and which is equal to 11. So L is equal to 11. So the new square that we have formed here the side of a square will be 11 cm because 44 cm length wire is converted in the form of square. So all the sides should be equal to each other.

[00:09:45]So we have to divide 44 into four equal parts and that's why the side will be 11 cm. I hope yeah yeah sure clear everyone. So the side of the square will be 11 cm. Moving ahead. Next question.

[00:10:02]Find the cost of fencing of a rectangular park of length 250 m and breadth 175 m at the rate of rupees 12 per meter. Per meter. Can you see this per meter? Met square is not there per meter is there. It means that we are talking about length and what is called fencing. Fencing means the covering the boundary. For example, I I'm having a plot a piece of land and I'm you know covering the boundary of piece of land by you know iron whatever you know wooden piece of iron blocks or whatever I mean brick wall so that is called you know fencing covering up the any piece of land from outside from the outside that is called fencing right so my question is find the cost of fencing a rectangular rectangle rectangular park so let's We have a park here. This is park. Rectangular park. And the length of the park is 250 m. Perfect. This is 250 m. Right? So if this is 250 m, it has to be 250 m. And the breadth is 175 m. Right? So you have length and you have breadth. Right? Now what is the cost of fencing? So let's say you are making the boundary using the iron wire or using the brick wall. Whatever you are making the boundary and this is called fencing. Making the boundary is called fencing. Right? So the cost of fencing is 12 rupees per meter. So let's find out the total length of the boundary first. Let's find out the total length of the boundary. So total length to be fenced to be fenced. Let's find out the total length of the boundary that needs need to be fenced that are fencing. So what will be the total length? 250 + 250 175 + 175. So if this is rectangle so we can write 2 into L + B. This is the formula for parimeter. So we have 2 into L is equal to 250 and breadth is equal to 175. Then calculate.

[00:12:15]So this will be equal to 5 7 5 12 carry 1 2 and 1 3 is carry four. So we have uh four 2. So this will be 5 2 10 0 2 4 5 and 4 2 8 total length of the boundary is 850 m. And what is the cost? The costing for fencing is 12 rupees of 1 m.

[00:12:36]And what is the total length that that to be fenced that is need to be fenced 850 m. So what will be the total costing? So, so total cost.

[00:12:50]So, total cost of fencing will be what? 12 into 850 rupees. 12 into 850. Please multiply this. So, 85 into 12. We can put 1 zero at the end. So 5 2 are 10 0 8 2 are 17 16 17 5 1 are 5 8 1 are 8 0 7 5 12 carry 1 8 and 9 10 Wow. So this is 1 0 2 0 and one more zero because we have ignored here zero but zero is there. So this is the total cost 10,200 rupees is the total cost for fencing this rectangular park.

[00:13:28]Hi sir. Hi Adil Lakshmi. Gohal Adil Lakshmi is back. Hi Captain Adita.

[00:13:35]Okay, very good. Welcome. So I hope this question is clear to you. Basically in this question there was a rectangular park of dimension length 250 m, breadth 175 m and this rectangular park is basically fencing. Fencing means making the boundary outside the park. Making the boundary and this is the cost for fence fencing 12 rupees per meter. So what will be the total cost? So let's find out the total length of the boundary and multiply by 12 and that is the total costing 10,200 rupees. Okay, moving to chapter number seven. Hello sir, make four algebraic identities. So Adilaxi uh for your kind information uh one one or two videos have already been uploaded on the channel of the chapter you are talking about that is algebraic identities. I have already uploaded. Go and watch those videos. Everything will be cleared because I have explained everything from basics from zero to advanc. So nothing is challenging there.

[00:14:34]Go and watch. Yeah sir. Unfortunately our school is still following the old NCI textbook. How is it making sense? You will be getting questions in your exam from your new textbook. So why they are following old textbook? Still don't I don't think it is making any sense for the student.

[00:14:51]Okay? Because the CBSC had changed the pattern. And you will be getting competency questions in your class 9th exam, final exam and class 10th value based question, application based questions. Right? So following I mean old NCERT textbook is not making any sense for me being a teacher. Okay?

[00:15:07]Okay. So let's this is all about the parimeter this chapter my dear. So this is very easy trust me the chapter measuring space is very easy. The questions are directly based on formula and most of the questions rectangle and square is there. some some question circle is also there. So let me uh introduce you about circle. So listen champion this is a circle here and uh this will be the center and this is called radius. Right? Now in circle if I ask you what is the parimeter of the circle? Formula for parimeter.

[00:15:41]So my dear champion there is very special formula. Parimeter means you know parimeter. Parimeter means the total length of the boundary whether it is square, rectangle, trapezium, parallelogram, rhombus or whatever. The parimeter of a circle means total length of the boundary. Right everyone? So the formula for parimeter of the circle is 2 pi r. This is the formula we generally use. And we have value pi is equal to 22x 7. Whenever you required as per your requirement you can put pi is equal to 3 22 by 7 or you can also put 3.14 these are the values two values it depends which values will be relevant for you as per the situation as per the question sometime you may put fraction sometime you may put decimal form okay now if I ask you area of circle so if I ask you area of circle so there is a formula very powerful formula pi r² so these Two formulas are very important. These two formulas are very important. Perimeter of circle is 2 pi r and area of the circle is p<unk> r². Please keep these two formulas in mind.

[00:16:51]Hi.

[00:16:54]Yes. Is it clear to everyone?

[00:16:57]Okay. Clear everyone. So this is all about circle. So clear. Now one more thing. If we complete this line, the line which is passing through center of the circle is called diameter. And the magical thing about the diameter, diameter is equal to this is complete diameter. And can you see diameter is equal to r + r. So diameter is the double of radius or we can also say radius is equal to half of diameter.

[00:17:23]Clear everyone? So these two formulas are very important. Who is this? Hi Gula Mustafa. Yeah. Hi. Moving ahead, chapter number seven. So champions, chapter number seven is basically the mathematics of maybe. You know when we use maybe, when we are predicting something, when we are talking about Yeah. It may be, it may be, it may be, when we are talking about some possibilities, some chances, chance to happen something, right? So we generally use maybe. If anyone any any friend of you is asking so will you be coming tomorrow for to play cricket in ground so you'll be saying uh maybe maybe so there is this chances there is some chances so maybe so basically in this chapter we are going to talk about we are going to talk about possibility possibility or we can say chance chance to occur something or we can also say this is combining these two words very you know systematic word is produced the new word combining these two and this is called probability in mathematical term this is called probability and what is the essence of probability again same thing possibility or chances so we are going to talk about here in this chapter what is the probability to happen something what is the probability to something occur so this is all about yeah hello everyone yes dear everyone So we are going to talk about these things.

[00:18:56]So the mathematics of maybe introduction you to probability and dear class 9th champions listen this topic will be carrying forward in class 10th also you guys will be studying this chapter this particular chapter in class 10th also. So try to understand the basics of this chapter I'm going to teach you here so that it will be helping you out in class 10th also. Okay. So please focus everyone. Okay. So look at the first question. First question.

[00:19:27]Rank the following events on a scale from zero to one certain and label each as impossible, less likely, even chance, more likely or certain. Give a reason for each ranking. Wow, what a question.

[00:19:46]Hi sir, in my school they just started it today. Very good. So this this session is very important for you. If you know little bit about this chapter, so this session is going to be very important for you because I'm not going to teach anything theoretical. I'm going to solve question directly. So please watch the video. Okay. So champions please look out the question here. So four conditions are given here and we have to find out the possibility probability and we have to rank which is having more chance to occur, which is having less chance to occur. This is the question here. So look at the first question. The sun will rise in east tomorrow.

[00:20:24]The sun will rise in east tomorrow.

[00:20:26]Everyone knows. Sunrise in east. Sunset in west. Everyone knows this. So this is 100% confirm my dear champion. If I ask you in which direction sun rises every day. So the answer is east. And in which direction sun sets every day. So sun always suns set in the direction of west. Sunrise is happens in east and sunset in west. Right? So the first information is the sun will rise in the east tomorrow. Everyone knows this. This is 100% correct.

[00:20:59]This is 100% correct. This is 100% correct. So the answer will be one. One.

[00:21:06]One for certain. Certain mean it is confirmed that it will happen. So for that we generally use 100% and 100% means 100 by 100 which is equal to one right everyone knows sun will sun no human being no one can control the movement of sun except nature except God. So everyone knows that in the next morning the sun will be rising from east. So this is 100% confirmed. So we are putting there one. Okay. It will snow in Mumbai in July. It will snow. It will snow in Mumbai in July. No one knows. It is not confirmed. If I ask you what will be the probability of this?

[00:21:43]Namaste sir G is Max Gaming. Wow. Hi namaste. Namaste. How are you champion?

[00:21:51]Yes. What will be the answer of this?

[00:21:56]Yeah tell me. Hi namaste. Who is this?

[00:22:00]Hi Mustafa. Hi everyone.

[00:22:03]Please tell me what will be the scale of probability of this second question.

[00:22:08]Very interesting question. Very literally this is very interesting.

[00:22:12]Second one tell me who is this.

[00:22:18]Okay.

[00:22:22]Tell me everyone what do you think? If I ask you what do you think?

[00:22:28]Who is this? How are you sir? Sharani Sai. Hi sir. Hi Sai. How are you?

[00:22:37]Hi everyone. Sai hello to you. Now do this question everyone please you have to rate the possibility from 0 to one basically yes tell me I'm waiting for the response in chat section everyone this is literally interesting question trust Hey, no one is there.

[00:23:25]Yes.

[00:23:27]Yeah. This is not possible, bro. The second statement is the it will snow in Mumbai in July. In July is it possible?

[00:23:36]Not at all. In July there is monsoon.

[00:23:39]There is you know scorching sun is there. So irritating sun so much of heat. So this is not possible. Not at all. So the probability is zero. Who answered zero? Let me check it once.

[00:23:52]Anyone is there?

[00:23:55]Namaste sir. Uh 1 2 0. Sai va is there sir. 2 0 3 1 uh 3 1 4 0 Okay okay okay let let's wait for others respond only Sai has responded here now the second is a tossed coin a tossed coin will land showing head now tell me what do you think if I'm tossing a single coin what will happen there is two possibility there is two possibility it may be it may be head it may be tail so no one knows this Huh? If you're tossing a coin. Yes. Anyone is there.

[00:24:39]Third how one will come. Listen shy.

[00:24:41]Listen listen listen. Our tossed coin.

[00:24:44]Our tossed coin will land showing head.

[00:24:47]No one knows. Now there is two situation. If you are tossing a coin there are two chances.

[00:24:53]It can be head, it can be tail. So there are two chances. So if we take the possibility if we calculate the possibility probability so the total number of possibilities are two and we are looking for head only so the probability will be 1 by 2 and 1x2 is equal to 0.5 because when you are tossing a single coin it can be head it can be tail so there are two chances anyone is there cap adita is writing so three third Third one I know sa what you are writing there. Now fourth question. An elephant will walk through your classroom today.

[00:25:35]An elephant will walk through your classroom today. You know is it confirmed? No one knows the who is this? Sai again same. So the question is an elephant. Yeah I'm waiting. I'm I'm so curious to know the answer of this fourth one from you guys. I want to check your mental ability. So what will be the probability?

[00:25:57]Is it confirmed? Is this confirmed that today an elephant will be passing through your classroom and who knows this? Yeah. Tell me what will be the answer of this?

[00:26:07]I'm waiting for others response. Only Sai has responded here.

[00:26:11]Who is this? Yes.

[00:26:18]Please tell me. An elephant. An elephant will be will walk I mean yeah will walk through your classroom today. Is it possible?

[00:26:34]Yes. Everyone please tell me who is this?

[00:26:45]Yes. What will be the answer of this question?

[00:26:51]No one. This is literally very interesting question guys. You should answer this question. See my dear champion. Who knows? No one knows. No.

[00:27:00]Zero. Yes. Fine. Perfect. Captain Adita.

[00:27:05]Very good. Zero.

[00:27:07]And elephant will walk through your classroom. How is it possible? The classroom is fully packed. Security guard is there. Entry gate is far away from the classroom. The school is having full you know high-rise boundaries. So how is it possible that elephant will be passing through classroom? So this is zero. So the answer is 1 0 0.5 and 0.

[00:27:28]This is the answer. Moving ahead. Next question. Question number two.

[00:27:32]Impossible. Yes. Yes. Is it impossible?

[00:27:34]So basically guys we are using zero for impossible.

[00:27:39]This is impossible.

[00:27:42]Right? This is impossible. Now if I talk about it will snow in Mumbai in July. It is also impossible. Yeah, there is little. No one knows if there is a mood of God like this. God wants to have snowfall. But yeah, it it looks according to weather forecasting, according to the you know previous stats, weather states of Mumbai, this is not possible. And this is here uh even chance less likely even chance even chance. Even chance this is called even chance. Even chance because 50% chance is there even chance. This is again not possible and this is certain certain 100%. The sun will rise from east. This is confirmed. Everyone knows this.

[00:28:22]Moving ahead.

[00:28:24]When a single six-sided dye is rolled once, do you know dice? You have played ludo everyone. You know you might be playing ludo with your family member. So basically there is a dye. If you know dye dye look like this.

[00:28:38]This is a dye. You know that cubicle cubical plastic structure when you like after shaking inside a box and you throw like this on ludo board and there will be numbers numbers are marked on this one here six for example I I don't know exactly the position of all the numbers but yeah I'm putting here one and here this wall also so this will be P three P three P three P three P three P three P three P three P three P three P three and that will be to their own front wall. So these are the numbers. So this is called you know die. So when a single die single six-sided die rolled once write the simple space and state the total number of possible outcomes why is each outcome equally likely?

[00:29:29]Listen champion. So what is called simple space? First understand the simple space. So basically what is simple space?

[00:29:39]Listen champion first understand the simple space. Simple space are all the possible all the possible all the possible outcomes.

[00:29:56]All the possible outcomes may occur may occur called simple space of any experiment. In any experiment, all the possible outcomes that may occur called simple space. For example, if we talk about this die, so basically simple space is written in this bracket, the middle bracket, right? So if we throw a die on a ludo board how many possibilities are there? How many possibility? It can show one basically we consider the number which is in up the number which is reflecting on the top surface. I know there are so many numbers in on side wall in the bottom but we generally uh I mean consider the number which is reflecting on top surface. Right? So the number can be whatever one it can be two it can be three it can be four it can be five it can be six. So these are the possible outcomes when we throw a single dice.

[00:30:54]Now the question is state total number this is why is each outcome equally likely. So my dear champion if I ask you probability of one what will be the probability of one. So how many one is there only one and how many total outcomes are there? So this is 1x 6. If I ask you what will be the probability that two will occur? Two will occur. So two is how many times? Only one time. So one and how many total outcomes? Six. So this is 1x six. If I ask you three. So how many threes are there? Only one. And total number of outcomes six. So again 1x 6. So the probability occurring all the numbers the probability of occurring one. The probability of occurring two.

[00:31:36]The probability of occurring three all are 1x 6 1x 6 1x 6. It means that the possibility of all the numbers are equal. So why why each outcome equally likely? Because because the number of one is one, the number of two is two uh one. The number of three is one. The number of four is one. Every number is reflecting one time. So the possibility will remain same. Moving ahead. Question number three. Look at the question number three.

[00:32:06]Write down the simple space. Simple space S for each of the following experiments. So we are having here three experiments and we have to write the simple spaces for all the experiments.

[00:32:18]So the first first experiment is rolling a die and tossing a coin all together.

[00:32:24]Oh my god what a question. Listen. So we have to write the total possible outcomes when for example me and my friend me and my friend I'm rolling a dice and my friend is uh tossing the coin. I'm rolling a dice here on ludo board and my friend is tossing a coin.

[00:32:42]arm arm means single coin and both activities are going simultaneously all together. So how many possibilities are there? Listen champion. When I am throwing a dice and my friend is tossing the coin. So what kind of possibilities are there? My dice can show any number 1 2 3 4 5 6 and this coin can show anything head or tail. So what will be the pair? The dice can show one and it can show head. The dice can show two, it can show head. The dice can show three, it can show head. The dice can show seven uh sorry six and it can show tail.

[00:33:20]So how many possibilities are there? So let's write it. So the first question is rolling a die. So my dear champion listen champion first of all if we talk about separate separate simple space for dice I'm writing here die. So simple space of D will be what? 1 2 3 4 5 6 right now if I ask you simple space of coin simple space of coin so what will be simple space of coin the simple space will look like head or tail so there are two separate sample spaces but here these two activities are going all together these two activities I'm throwing a dice and simultaneously my friend is throwing a coin both activities are going all together and we have to look on both the results and we have to match what exactly is reflecting there. So when this rolling dice and tossing coin both are going on together.

[00:34:22]So what are the total possibilities of simple space? So look champion one head one head similarly two head three head four head five head and six head.

[00:34:47]Similarly now put two two head three head. So three head is already there. So only this will be there.

[00:35:02]Now for tail for tail. So one tell two tail, three tell, four till five tail and six tail. So these are the possibilities when both the activities are going on all together. Someone is throwing a dice and someone is throwing a coin and both activities both experiments are going together.

[00:35:35]Coin 1x2 die 1x 6 have patience champion. So we have to write only sample space. We don't need to find anything. We have to write the sample space. So the these are the sample spaces. Now question number two.

[00:35:47]Choosing a random integer between minus5 and + 5. So what will be the sample space for this?

[00:35:54]For this second first is choosing a random integer between minus5 and 5. So my dear champion so if we talk about numbers between -5 and 5 so the numbers will look like - 5 -4 - 3 - 2 - 1 0 1 2 3 4 and this is 5. So these are the numbers these are the numbers between -5 and + 5. So the simple space will look like -5, -3, -3, -2, -1, 0. Now positive value 1, 2, 3, 4, and 5. I hope this is clear to you all. -5, -4, -3, -2, -1, 0, 1, 2, 3, 4, 5. Clear everyone? But the question is choosing a number num random integer between these two. So in that case we have to exclude this one. So these will be considered min -4 to 4 only because we are talking about integer between minus5 and five. So if we talk about between minus5 and 5. So these numbers will be considered from minus4 to four only. Okay. Moving to question number third. I hope everything is clear to you all. Hi. Hi. Fact. Okay.

[00:37:13]Okay. Look at the third number question.

[00:37:15]Drawing one ball at random from a box containing green and red ball. Drawing one ball at random. So basically champion listen here we have a box and the box containing green and red balls.

[00:37:32]How many balls are there? Two balls are there. So what will be the sample space?

[00:37:39]green ball and other one is red ball. Right? So this will be the simple space. Green ball and red ball. I hope this is clear. So what is simple space? Simple space are called all the possible outcomes when an experiment is carried out. When the experiment is done, all the possible outcomes are called simple space. So this is the sample space of first question. This is the sample space of second question. And this is the sample space of third question. Moving ahead, look at the question number four. A box contain Okay, so there is a box contain five green ball. Okay, green. Okay, five green balls. So, let me use green ball itself.

[00:38:24]H 1 2 3 4 five green balls and seven red balls. Okay, seven red 1 2 3 4 5 6 and seven. How many red balls? Seven red balls. Five green balls. Five green balls and seven red balls. One ball is random. One ball is drawn at random.

[00:38:47]Find the probability that the ball drawn is this. First let me tell you the formula for probability. How to find probability? So there is a formula in probability and the formula look like listen champion. Probability of any event is equal to total number of favorable outcomes.

[00:39:11]Total number of favorable outcomes divided by total number of outcomes difference total number of favorable outcomes divided by total number of outcomes. So basically this is the formula we use to find out the probability of an event. What is fabricable? Fabriable is what we are talking about green red either green or red these are the fabricable. Who is this? Myself Sana aesthetic with Suana.

[00:39:44]Hi Sana welcome to Dsha Andu platform.

[00:39:47]So the probability of any event we have this formula total number of favorable outcomes divided by total number of outcomes. Now what is favorable? These are the fabricable. So there is a box and this box contains five green balls and seven red balls. Now when we are picking up a ball randomly, I mean without looking at the ball, without looking at the box, we are picking at the ball randomly. We are picking up a ball randomly. So this is called random you know picking up. So what will be the probability of green ball? So here the event is I'm solving first question. The event is to get a green. This is the event to get a to get a green ball. This is your event champion. Just a second everyone.

[00:40:37]Okay. So to get a green ball, this is your event. So what will be the probability? Probability of this event.

[00:40:45]Green is your favorite. And how many green balls are there? Five green balls.

[00:40:49]And this is total number of outcomes. So how many total number of balls are there in this entire box? So total number of work 7 + 5 and that is equal to 12. So this is the answer 5 by 12. Second question similarly red ball. So what will be the probability of red ball? P red I'm writing here P red. P red ball.

[00:41:09]So now red is your favorable. How many red? 1 2 3 4 5 6 7. So we can put here 7 divided by 12. This is the answer. Third question.

[00:41:21]Either green or red. So when we are picking the ball randomly, it can be green or it can be red. This is our favorable condition. If the ball is red or green, either red or green. So both is fabricable here. Both are fabable. So P and we can mention here either green or red. Either green or red. So both will be combined. So 7 + 5 is 12 and 12 + 12 that is equal to 1 and 1 means 100%. If this is your fabric favorable condition when you have picked a ball the ball can be green or red. So everyone knows no because there is only two color of balls. So when you are picking a ball so ball may be red or maybe green this is confirmed and that we are talking about. So that will be 100%. Fourth is probability of getting blue ball. Oh my god. No blue ball is there. Only we have red and green color balls. There is no any blue color ball.

[00:42:24]So why we are I mean bringing this blue in conversation. The blue is don't even exist. There is no any blue color ball.

[00:42:32]So the number of favorable outcome is zero.

[00:42:36]There is no blue color. No blue color ball. No blue color balls.

[00:42:44]And if no blue color balls is there, it means 0 by 12. And 0 by 12 is equal to 0. No chance. This is called no chance.

[00:42:54]And we can say impossible. This is impossible. If the if the box contain only green and red color of balls, how is it possible to pick a blue color? Are we a m magician? We are not a magician.

[00:43:07]So if the box contain only green color and red color ball. So there is no any possibility to get a blue color from the box. Moving ahead. Question number five.

[00:43:16]Okay.

[00:43:18]A coin is tossed 100 times and heads appears 58 times. Okay. Find the experimental probability of getting ahead. Okay. Uh how does it compare with the theoretical uh probability and why are two values different? This is a good question. So in this question you guys will understand the difference between probability experimental probability and theoretical probability. So this is a good question because this question will help you out to understand the difference between both. Okay. So basically let's talk about experimental probability first.

[00:43:54]So my dear champion listen experimental probability is what?

[00:44:04]This is experimental probability. The experiment that is going on and the experimental going on is a coin is tossed 100 times. And how many heads appears? 58 heads appears. In 100 toss in 100 toss 58 times heads appears. So this was the experiment. So if we calculate the probability of this condition. So this is called experimental probability because the first line is experiment is an experiment. So how many times head is appeared. So what is the experimental probability of getting a head? So this will become 58 number of we are talking about head and how many times head appears 58 times. So number of divided by total number of terms. So 58 divided by 100. Now can you please cancel this?

[00:44:53]So 2 2 4 29 and this is 50. So we have 29 divided by 50. This is your answer experimental probability because this probability is of this particular experiment. Now moving to now moving to uh theoretical probability. So what is called theoretical probability?

[00:45:14]Listen champion. So basically theoretical probability is something when we use that particular thing in our day-to-day life. For example, we are talking about a coin. So we generally use coin in games in sports. Which team will start batting? Which team start will balling. So there is a procedure which carried out in beginning of the match and that is called toss. So generally we toss. This is theoretical use of the coin. So when we consider one coin, when we talk about single coin, one single coin, so that is called basically theoretical probability. So how does it compare with the theoretical? So we are talking about head. So when we toss a coin, for example, a coin. So what will be the probability of occurring head? So that is equal to 1 by 2 and 1 by 2 means what? That is equal to 50%. So this is called experimental probability and this is called theoretical probability. And and why are two values are different?

[00:46:20]Because here the total terms two and here same procedure is going on so many times 100 times and this is for single coin. Clear everyone? So this is experimental probability 29 by 50 and this is basically theoretical probability. Moving ahead question number six. Two coins are tossed together. Write the simple space and find the probability of okay. So basically we are tossing two coins.

[00:46:46]Listen I have one coin and my friend has one coin and both I myself and my friend both are tossing a coin together. So just imagine when we are tossing two coins all together. So how many possibilities are there? My coin might show head and his coin head head tail head head tail tail tail head. So there are few possibilities. So basically uh the number of simple spaces the number of outcomes for coin carries this formula 2 to power n. This formula plays very important role. So my dear for single coin if we toss single coin so basically n will become 1. So 2 to power 1 is equal to two. How many possibilities will be there? Two possibilities head and tail. But when we toss two coins all together, n will become two. And if we put here 2 to power 2 and 2 to power is equal to four.

[00:47:44]So how many possibilities are there?

[00:47:45]Four possibilities are there. How? Let me show you. So when we are tossing coins together simultaneously. So first coin may show head and second coin also may show head. So head head tail tail head and tail tail. So these are the possibilities when we throw when we throw three coins all together. When we toss when we toss three coins together so there will be probability 2 to power three and 2 to power 3 is 8. And there is very special technique that I usually use to write the total possible outcomes when three coins are tossed simultaneously. So first write this line at one gap. Head tail, head tail, head tail and head tail. Count 1 2 3 4 5 6 7 8. Now write the values at the gapping of two. Head head tail tail head tail tail. Now write the gap. Write all the values at the gapping of four. Head head tail tail tail tail. So these are the simple spaces. when three coins are tossed simultaneously. But here in this question we are talking about this. Look two coins are tossed together. So we are talking about this. So now write the simple spaces. So simple space is done for this question. This is the answer.

[00:49:09]Okay. Now find the probability of this first. Okay. So I'm solving the question here this side. Uh because it was very important for you to know how to write the simple spaces when one coin is tossed, when two coin is tossed, when three coins are tossed. Okay. So first question look so we are talking about this. So we are going to focus only on this. And the first question is what will be the probability? What is the probability of getting exactly one head in all these four? Exactly one head. So exactly one head is here in this outcome and exactly one head is here. This outcome we will not consider this because the question exactly one head.

[00:49:47]So exactly one head P probability of exactly one head we have one head we have is equal to what and that is equal to 2 divided by total outcome 1 2 3 4 2x 4 and which is equal to 1 by 2 this is the answer. Second question, two heads. Two heads only one possibilities are there only. So the number of outcome probability of two heads. So what will be the probability of two heads? This is equal to one and favorable outcome is one and total number of outcome is four. So 1x4.

[00:50:28]Third question. Third question. At least one head. So at least one head here, here also, here also and here also. This will also consider because we are talking about at least one head. So at least one head here, here and here. So three probability of at least three will also count. Three heads will will be also count and two heads will be also count because we're talking about at least one head. So at least one head is here here and this will be also counted. Okay. So at least two head and the formula will look like the value 1 2 3 the total favorable outcome is three and total number outcome four.

[00:51:08]Fourth question. No heads. No heads. We don't require no any head. No head. So no head. This is only possibility. Both should be tell. If we required no head, so both should be tell. So the probability of no head means both should be both coins should sail only. So tell is one and total number outcome for this is the answer. So this is the solution of this particular question. Clear everyone?

[00:51:36]Moving ahead. Question number seven. A single dice is rolled once. Okay. So first of all when we roll a dice. So total number of possible outcomes. This is the sample space. One 2 3 4 5. These numbers are generally marked on a die.

[00:51:54]So six possibilities are there. Find the probability of getting a number uh greater than four. So first question the probability will be a number greater than four. So how many numbers are greater than four? This and this. So this will be two favorable outcome. This is the favorable condition. So favorable outcome two and total number of outcome six. So this will cancel. So the answer is 1 by 3. Second question.

[00:52:22]Second is an even number. How many even numbers are there? Two is even number.

[00:52:26]Four. Four is even number and six is also even number. So three total favorable outcomes. These are the even numbers. two and four and six. So favorable outcome is three and total number of outcome in this simplest space. So it will cancel. So the answer is 1 by two. Third question.

[00:52:45]Third question. Third question a prime number. Do you know prime number? One is neither prime nor composite. So please exclude one. So first prime number is two. Second prime number is three.

[00:52:58]Fourth uh first prime number two. Second prime number three. and fourth prime number will be five. So how many prime numbers are there? Again three divided by 6. So it will cancel. So the answer is 1 by 2. Fourth question. A number less than seven. All the numbers are less than seven. You can focus there. All the when we are throwing a die on a ludo board the numbers appearing all the numbers are less than seven. Because on ludo the numbers marked is from 1 to six. All the numbers are 1 2 3 4 6. These are the numbers marked on the ludo die. So if we talk about a number less than seven. So all the numbers are less than seven.

[00:53:39]All the numbers are less than seven. So the formula will look like the probability will be all the numbers are favorable because we are talking about number less than seven. So if we are talking about number less than seven, number less than seven, all the numbers will be considered. Right? If all the numbers will be considered. So my dear champion we can write six divided by 6 and which is equal to 1 and this is the 100%. If we throw a die sir uh is it who is this? Thank you by the way Ankush. Thank you so much. Okay so this is the answer. I hope this question is clear to you all. So writing the sample space is very important. How many possible outcomes are there? How many possibilities are there? Moving ahead.

[00:54:21]Question number eight. A number is chosen at random from a number 1 to 20.

[00:54:27]What is the probability that the chosen number is this? Okay. So there are number from 1 to 20. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 and 20. We have these numbers. The question is what is the probability when the chosen number is we are selecting a number we are choosing a number randomly. So what will be the probability that the chosen number is a prime number. So first question what will be the probability of getting a prime number? So how many prime numbers are there champion? Do you know prime number? The number which can be divisible by one and itself. Yes.

[00:55:17]Very good. A so do you know prime number? The numbers which are having factor only one and itself for example 17 11 5 19 23 all the numbers are prime number because they can be divided by only one and itself.

[00:55:33]If I ask you 19 can be divided by 1 or 19 can be divided by 19. So only two possibilities are there. That's why 19 is called prime number. So now please find out how many prime numbers are there in this group of in bunch of this number. One is neither prime nor composite. So please who is this? Hi man. So one is neither prime nor composite. So please ignore. So the total prime number will be two is a prime number 1 2 3 4 5 6 7 8. So total prime numbers are eight divided by how many total numbers from 1 to 20? 1 2 3 4 5 If you counting, if you write the counting, that is obviously 20. So now we can cancel 2 4 are 8 5 4 are 20. So the answer will be 2x 5.

[00:56:25]Second question.

[00:56:27]Second question uh a multiple of five.

[00:56:31]What will be the probability of getting a number multiple of five? You know multiple of five. Multiple of five means what? The table of five. Multiple of five means table of five. Five 1's are 5. 5 2's are 10. 5 3's are 15. 5 4 are 20. How many numbers? 1 2 3 4. So this is 4 divided by 20. Four will cancel by five times. So this is equal to 1x 5 is the answer. Third.

[00:57:01]Third is a perfect square. You know perfect square whose root is possible?

[00:57:10]Yeah. Yeah. Sure. without any delay.

[00:57:12]Come on. Thank you, Ankush. Okay. So, this is the bunch of number and if you're picking a number randomly, so what is the probability of getting a perfect square? Do you know perfect square? These are the perfect square.

[00:57:26]Four is called perfect square. 9 is perfect square. 16 is perfect square because their root is possible. If you write uh roo<unk>4, roo<unk>4 is equal to 2. If you write roo<unk> 9, roo<unk> 9 is equal to 3. If you write root 16, roo<unk> 16 is equal to four. So such numbers are called perfect square. So what will be the probability of getting perfect square from these bunch of numbers? So the probability of getting a perfect square.

[00:57:56]So how many numbers? I think three numbers. 4 9 and 20. 4 9 and 16. Right?

[00:58:00]So three numbers we have the numbers perfect square. We have three numbers.

[00:58:05]So we can write here three divided by how many numbers total? 20. So the answer will be 20. 3 by 20. Yes. Hi everyone. Hello everyone. Is it clear to all champions?

[00:58:16]Is this question clear to all? Any doubt to anyone? Please ask.

[00:58:21]I hope everything is clear.

[00:58:24]So the student who knows the property of prime number, perfect square number, multiple for both student this question is nothing. Literally nothing.

[00:58:36]Okay, clear everyone? Moving ahead.

[00:58:38]Question number 10. A dice is rolled 60 times and the number a dice is rolled 60 times and the number six appears eight times. Find the experimental probability of getting a six. Very easy question. I have already solved such question here.

[00:58:53]uh yeah this experimental probability and uh the difference between experimental probability and theoretical probability now I'm giving you this question for you to solve this is homework for you everyone homework solve this question and please let me know the answer of both okay now ID champion a very big announcement I mean I'm I'm feeling literally proud from within and I'm very happy to announce in front of you guys that this you know on the basis of the standing legacy of vantu again we have proved this year in the year 2026 if we talk about J result neat result J advanc result J men's result case set result again vidantu has proved why vidantu is unique in all yes so outstanding result in neat so we have produced all India rank 779 triple digit rank champion in jungle category and it's a big achievement for vidantu whole entire family all India rank 563 all India rank 526 So this is Shiran, Aayush and Ainas scored secure all India 426 and this is Shahak Vishut Heant is there and Murugeshwaran is there. So moving ahead from neat aspirin to future doctor. So congratulations to everyone and look at this result and this student is secured. The name is Sarak Patil and the rank is all India rank 10 champion getting all India rank 10 in a reinit exam. If you go and ask the senior the level of question that that all the neat aspirants got this year was literally so lengthy and tough but still the vantu students again shined with colorful rank and that is general category 10 rank from two-year classroom program and you know many more the result is ultimately speaks so look at the result the number is still counting J1s all India rank 178 so so many ranks are there 27 ranks we I mean we have produced this year 27 Seven rank in top thousand champion top thousand all India rank. So this is the big achievement again this year. Now solid preparation this is the principle on which all the faculty members are working and we believe in you know delivering quality sessions quality content for you champions. So two J means 2026 2200 plus students got qualified for J advance this year and look at the result. The result itself speaks. Okay. So outstanding. So congratulations to everyone my dear champion. So if you are looking forward to uh prepare for J if you are having dream to achieve uh government city need or J my dear champion. So very soon we are launching on this channel Titans batch. The batch name is going to be Titans batch on every Sunday there will be sessions of maths. So from 9th and 10th onwards we'll be teaching you basic maths and that will be helping you out to build up strong foundation that will be I mean that so that you guys could uh ensure yourself uh for the strong preparation to correct J or NET after 2 to three years in your future. So from 9th this is the right place this is the right time to start your preparation champion. Some student plans for J and Nit after completion of their class 12th and PUC. This is this is the right time honestly. Okay. So our student golden victory in Olympiad. So this is the Olympiad. So we are not in uh you know we are also ahead in Olympiad as well not only in Jit. So international physics olympiad that was held here this year. So Riddesh Benlay from Vidantu and look at the result all India rank he also uh you know in APO 2025 he's won silver medal in IPO 2025 gold medal and again gold medal and he secured all India rank 18 in J advance 2026 again these are the you know toppers this year one more thing my dear champion big announcement about AIO so one very powerful platform we are launching on Vidantu AIO and The AIO means all in one. All in one champion.

[01:02:55]So my dear champion if you are having any query any problem in any particular chapter. If you want to get NCERT solution of any particular chapter if you are having any doubt in any topic my dear you can raise your doubt. So in all all in one platform my dear you'll be getting complete academic solution. So go and enroll today that is free my dear and you can go and browse on Google. you can directly write all in one CBAC class 9th class 10th and you will be directly uh directed to interface of vantu. So this is very you know big initiative I would say and very powerful initiative for all the student who is in class 9th and student who is I mean board student preparing for their board exam class 10th CBSC 2027. This is very important.

[01:03:41]So without any delay go and enroll yourself in all allin-one money platform champion. Thank you so much for having me in this live session. Thank you so much everyone. Bye-bye. Take care of yourself and take care of your parents also. See you soon in the next live session.