Maths P2 - Probability Made Simple || Fail no More.

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[00:00:00]Hello. Greetings.

[00:00:03]I've got these two wonderful questions that I want you to get and understand.

[00:00:11]Probability probability. A question can come like this or a question can come like this. So, I want you to get and understand me very well and clearly. So, I need your total attention.

[00:00:31]If it is possible, I would love it uh these questions being written down.

[00:00:37]So, I want you to write down these particular questions for revision purposes.

[00:00:45]This video is public. I've shared it on all social media platforms. So, you can help me by sharing this even to your friends.

[00:00:58]And make sure that you follow, like, and comment. Let me know how this lesson is going to be. All right. So, the question is saying Mutola and Mwambi were to be selected as members of a netball team. The probability of selecting Mutola is 7/8 and that of selecting Mwambi is 9/10.

[00:01:30]Find the probability that only one of them is selected.

[00:01:37]When you see this kind of a question, the way it is, have you seen? You are being given the probabilities of the people or things being mentioned and you are told to find the probability. So, meaning that there is no need of us finding what we get to call a tree diagram. There is no need for that. I guess we are following each other.

[00:02:04]For us to answer this question, we are told to find the probability of selecting who? Mwambi. So, the probability of selecting Mwambi is 9/10.

[00:02:16]Now, what is the probability of not selecting Mwambi? So, the probability of selecting Mwambi is this, then what is the probability of not selecting? So, the probability of what? Not. So, I'm going to say the probability of not selecting. So, not selecting. Not selecting who? Mwambi. The probability of not selecting Mwambi. What do we do?

[00:02:47]We know when you are given one probability and you are told to find the other probability, we just subtract from one. So, we say 1 9 over 10.

[00:03:02]What is the answer? 1/10. So, the answer is 1 over 10. This is the probability of not. So, not selecting. This is the probability of not selecting Mwambi.

[00:03:19]Have you seen? The probability of not selecting Mwambi is 9/10.

[00:03:25]Now, the probability of selecting Mutola is 7/8.

[00:03:32]What is the probability of not selecting Mutola? So, I'm writing these things and these are the same things that are going to help us now answer this question. So, not selecting. Not what? Not selecting Mutola. What is the probability of not selecting Mutola? We get the probability of selecting Mutola, which is 7/8. We subtract it from one because we know that if I tell you to say that the probability of going to school tomorrow is 3/5, what is the probability of not going to school tomorrow? You're going to say 1 - the given probability. This is what I'm doing even here. So, I say 1 7 over 8. What is the answer? 1/8. We are getting 1/8 as the answer. So, 1 over 8. After we do this, this question now we've just dissolved it like this.

[00:04:43]Panguka pamandipa panaka. What we are going to do now, we just go straight now.

[00:04:50]Only one of them is selected. Only one of them is selected. So, we say solutions. This is how you are supposed to answer. Question inatwi natwi angusha. So, only one of them is selected. So, I'm going to do this. Only one of them is selected. So, we get this one. So, if we select Mutola, so Mutola, that is 7 over what? 8.

[00:05:22]Times the probability of not selecting the other person. So, the probability of not selecting Mwambi is what? 1 over 10 like this.

[00:05:34]You say plus. Here now, we are going to select Mwambi. The probability of selecting Mwambi is 9/10 times the probability of not selecting the other person because the question is saying only one of them is selected.

[00:05:52]Here, we selected who? Mutola and we did not select this one. Here, we select Mwambi and we get we multiply it with the probability of not selecting Mutola, which is 1 over 8 like this. You get your calculator, work out this. You are done. Very simple. Have you seen? So, the key thing is once you are given the probabilities of selecting them, we find the probability of not selecting them.

[00:06:23]So, what are we doing now? We get this one. So, what is it? 7 over 8 times 1 over 10. What is the answer?

[00:06:35]The answer is 7 over 80. 7 over what?

[00:06:40]80. Plus C. We are just getting a calculator here. What is the 9 over 10?

[00:06:49]Times 1 over 8. What is the probability? I'm getting 9. So, I'm getting what? I'm getting 9 over 80.

[00:07:02]If I add here, what answer am I getting?

[00:07:05]Plus. So, if I add, what answer am I going to get there? What is the answer?

[00:07:11]The answer I'm getting is 1 over 5. This is the answer. You are done. So, this is the probability of selecting only one of them. So, when you are the two of you, then you are told to say find the probability of selecting only one of you. If I select you, I get the probability of not selecting the other one. Plus C. I select the other guy times the probability of selecting you. Have you seen? So, this is what is happening here. I guess you are able to see the logic here. Then we go to this one. NONE OF THEM IS SELECTED. You just get the probability of not selecting uh none of them. So, we go to this one. The probability of not selecting. None of them is selected. So, the probability of not getting any of them which is just what? We just this one. 1 over 10 times 1 over 8. The answer is what? 1 over 80 as the answer. This is the answer you're going to get.

[00:08:23]So, selecting only one of them. This is where now we get to multiply the prob- prob- the probability of not selecting the other one. But here, where we are told that none of them is selected.

[00:08:39]Meaning the probability of not selecting Mwambi is here direct. The probability of who? Not selecting Mutola is here direct. So, this is how you answer a question like this. So, if you are looking for tuitions, you want someone that can help you understand these things well or well. You can consider joining Harrisonite Learning Academy online school of tuitions. We are a school for online tuitions. So, you can get in touch with me on this number in Zambia.

[00:09:14]Plus 260971066747.

[00:09:21]This is my number. I'm going to help you. 0971066747.

[00:09:28]Let us go to this one that is here. So, I'm going to write my number so that you get to see it. Let me write it here.

[00:09:35]This is my number. If you want tuitions, we are going to make sure that we help you. I'm a [clears throat] full-time online tutor here in Zambia.

[00:09:47]A box contains three black and two white marbles of the same size.

[00:09:55]A marble is taken out at random from the box and not replaced. A second marble is then drawn. Calculate the probability that both marbles are white, the probability of different colors. A question can come like this and a a question can also come like this. If a question comes like this, just know that you need to draw a tree diagram. What do I mean when I say like this? Where you are told Okay, a box contains this, a box contains that. A number is given one up to 10.

[00:10:33]The probability of even numbers, the probability of odd numbers. Those type of questions, you draw a tree diagram.

[00:10:42]Like this one. So meaning that we are just going to go direct. We just say, "Okay, a tree diagram is having two branches, the black one and the white one." Like this. Let me see this is recording.

[00:10:57]To us my tonight Okay, so It is recording like this. This is what we have. Then, what is the next thing to do?

[00:11:09]Black, there are many? Three. White, there are two. Total number of these marbles is five. So black, there are three.

[00:11:19]Over the total number, five. White, how many are there? Two. Total number, five.

[00:11:28]So the second selection now is where we get to say that we assume that the marble that was picked was a black. Have you seen? So even here, that branch will be like that. Black, white. So when we go here, we are going to assume that the marble that was picked was black. So only this black is going to change. So there are many? Three. We get one, two. Total number, four. Because from the box, there are five. We pick one, which is a black one. So even the total number has changed four.

[00:12:13]The white ones will remain the same, two over four. The total number has changed.

[00:12:19]When we go here, only the white marbles are going to change. The black ones will remain the same. We forget about this.

[00:12:28]We go here. So here, how many white? We remain with one. Total number, four. The black ones, there are three. So three over four.

[00:12:41]This is what you need to do. So this is what we get to call a tree diagram. So here, this is outcomes. We say black black. Here, black white.

[00:12:56]Here, we say white black. Here, what are we having? White white. That is it.

[00:13:06]So this is what we call a tree diagram.

[00:13:09]I guess you've heard of this. This is a what? A tree diagram. Just like this, as simple as this. So once you draw a tree diagram, it means that everything uh has become so simple and you just have to make sure that you get everything correct because once you draw a tree diagram, you I guess we are together.

[00:13:32]So here, what are we going to do here?

[00:13:36]So what are we going to do? What are we going to do here?

[00:13:41]Find or calculate the probability that both marbles are white. Both marbles are what? White. Where do we have white white? Here. So that is one. The probability of white white. So white white is just these two. White white. We just multiply these two. Two over five like this times the times what? One over four. What answer are we getting there?

[00:14:13]What is the answer? What answer are we getting there? When you multiply. Just get your calculator. Two over five times one over four. What answer are we getting? One over 10.

[00:14:29]This is the answer, one over 10. This answer is already simplified. Someone will say, "What if I multiply two times one, I'm getting a two over five times four, that is 20."

[00:14:44]Two there, it is one. Two there, it is 10. Have you seen? So it's better you go with a calculator where you get the answer that is already simplified.

[00:14:53]We go to number two.

[00:14:56]Have you seen number two? We are moving together. So this is it and this is what you need to get. So calculate the probability that both marbles are of different colors.

[00:15:08]Both marbles are of different colors. So what you are supposed to do or what you need to get here is that different colors here. Here, we go there and there. Have you seen? So this is the probability of different what? Colors.

[00:15:29]What we do, we get this one. That is what? This one. Meaning this and that.

[00:15:35]We multiply these two. Have you seen?

[00:15:38]Black white. We multiply these two.

[00:15:40]Three over five multiplied by a two over four. We do this. Then I say plus. Have you seen? This is what I need to do.

[00:15:51]Plus, I go to this one, different colors here.

[00:15:56]White black. White black. So I'm getting this one and that one. That is two over five times the three over four. This is what I'm doing. Have you seen? So then from here now, what I need to do now, I need to multiply. Get my calculator. I say three over five times two over four. What answer am I getting? This part, I'm getting three over 10.

[00:16:31]Plus.

[00:16:33]I go this side. I'm just using my calculator. DON'T SAY JUST MULTIPLY DIRECT. That answer won't be simplified.

[00:16:40]We want an answer that is going to be already simplified. Two over five times three over four. What is the answer? Three over 10.

[00:16:55]Three over 10.

[00:16:57]So if you add here, have you seen? If you add there, we are adding three over 10 plus three over 10.

[00:17:05]What answer are we going to get there?

[00:17:08]We are going to get what? The answer, final answer is going to be three over five. This is the answer. This is what you need to do.

[00:17:20]The same way I've answered this, this is how you are supposed to answer. Even in an exam, as simple as this. Have you seen? This is something that is so simple. I don't expect anyone to fail such questions. I guess you've you had followed me so well and you saw how I was answering this. So this is how you are supposed to answer and this is how things are supposed to go. This is your full-time online tutor. We are the online majors. So we are here to help you get a distinctions in different subjects. I don't only teach mathematics, I teach almost all the subjects. So maths, biology, civic education, R.E., science, we've got commerce, we've got R.E. 2046, additional mathematics. Even for form one, you can join. So this is what I wanted us to discuss. This is your full-time online tutor from Zambia Tutors and