U8 2 Simple Event Probability

Añadido: 2026-05-05

[00:00:01]Unit 8, lesson 2, simple event probability. Today's essential question is, how do you describe the likelihood of an event?

[00:00:12]Let's take a look at what simple probability is.

[00:00:17]Simple probability is the expressing the likelihood of a single event as a ratio.

[00:00:23]So, let's highlight single event, it's only one, as a ratio. So, here on your right, you have this nice line chart. We have a zero here, and all the way down you have a one. And right in the middle you have 5/10. So, 5/10 is the halfway mark, and if you look straight down here, it says a 50/50 chance. So, we're talking about flipping coins, or drawing the right card out of a deck. So, when do you have a 50/50 chance?

[00:00:53]Well, it's as likely as not, or an even amount. So, let's highlight the word even.

[00:01:01]Let's highlight the the phrase as likely as not. So, it's 50/50, or you have a 50/50 chance. So, 5/10 as a decimal, if you multiply 5/10 * 100, it would give you 50 percent on the calculator.

[00:01:21]Now, if you go all the way down to the right side where you have a one, if you multiply one by 100, you would get 100%.

[00:01:30]And that's said to be certain.

[00:01:35]So, if a coin had heads on both sides, and you called the heads, you would know for a 100% chance that you would get heads because there is no tails on the coin.

[00:01:48]Let's travel all the way back down to the left where you have zero.

[00:01:53]Zero * 100 is zero percent.

[00:01:57]This means impossible.

[00:02:03]There is no chance of it happening, absolutely none.

[00:02:07]All right, so we have some leftover categories here. We have unlikely, and you can see unlikely is from this arrow head here all the way to this arrow head here, right before the 50%. This is the unlikely area.

[00:02:24]So, 25/100 * 100 is 25% chance.

[00:02:31]Now, in this unlikely category, you have highly unlikely.

[00:02:43]You have likely, or sorry, unlikely.

[00:02:50]And if you travel over the top of the 50% on the other side, you can see you have a 75/100. Well, 75/100 * 100 is 75 percent.

[00:03:01]And now you're entered into the likely side of your chance.

[00:03:06]So, you can see the arrow again going from the middle to the end.

[00:03:12]And anywhere in there is called likely.

[00:03:16]So, this 50% to 75%, you have a likely chance of it happening.

[00:03:23]And then the last part is highly likely.

[00:03:36]Probability is a ratio of favorable outcomes to all possible outcomes.

[00:03:43]So, let's highlight favorable, and we'll talk more about that later, outcomes to all possible outcomes. That's your ratio. So, the top number is going to be your X, so your favorable is going to be your X, and your all possible is going to be your Y. And just a reminder that as ratios, we have X to Y is one way to write it, or X to Y with a colon, or X to to Y, just like a fraction. You've dealt with this before in past units, so it's just a reminder. Or, you can change into a percent.

[00:04:27]All right, let's jump into the heart of the lesson here. It's finding the likelihood of a favorable outcome.

[00:04:36]So, all possible outcomes, I have it in red, you may want to highlight that on your paper.

[00:04:43]Are referred to by as by the sample space.

[00:04:53]The sample space uses a capital S for sample space.

[00:05:00]Here we have a table. We have all outcomes right here. We have the sample space right here. And then there's a blank part right here. We'll talk about what that means in a little bit. And then we have a couple of um diagrams over here that we'll use in a little bit.

[00:05:15]Our first um likelihood, or favorable outcome, sorry, not favorable, but all possible outcomes is flipping a coin. So, what's the sample space? How many different things can happen when you flip a coin?

[00:05:28]Well, there are only two, a heads or a tails, so we're going to put two.

[00:05:32]That's all of the possible outcomes.

[00:05:34]There are two of them. So, what are they? Well, we could get heads, or we could get tails. Those are the only options on flipping a coin.

[00:05:47]Let's move on to rolling a die.

[00:05:49]That would be six. There are six sides of a die.

[00:05:54]And what are they?

[00:05:56]A one, two, three, four, five, and six is our sample space. So, any of those can happen while you're flipping a die.

[00:06:07]As we move on to drawing a card out of a 52-card deck, so write 52 cards.

[00:06:14]And in the 52-card card deck, we have hearts, diamonds, clubs, and spades. Each of those has 13 cards.

[00:06:26]So, just put an arrow.

[00:06:30]And if you do 13 * 4, you would get 52.

[00:06:35]All right.

[00:06:37]Put a line here.

[00:06:39]What type What type of cards are in a deck of cards? Let's just take the spades for instance. You have an ace, you have a two, three, four, five, six, seven, eight, nine, 10, and then you have jack, queen, and king. So, try to fit them all in there. There's quite a few. Count them to make sure you have all 13. 1 2 3 4 5 6 7 8 9 10 11 12 13.

[00:07:14]So, each card, or each suit, these are called suits, has 13 cards, and each of those has all of these here.

[00:07:25]Let's move on to a spinner. Well, it depends on the spinner. That's why we have the quotation marks here. If we look over at the diagram, you can see that this diagram has eight spaces. So, we count them 1 2 3 4 5 6 7 eight spaces.

[00:07:41]So, we'll put eight here. There's eight different things can happen on that spinner.

[00:07:46]And what do you see? Well, spinners could be by color, they could be by number, or anything else. On this particular spinner, you have eight pieces. So, maybe if they're labeled by numbers, it'd be 1 2 3 4 5 6 7 8, or maybe be by colors.

[00:08:07]So, it just depends on what it is.

[00:08:10]This next one, we have colored marbles.

[00:08:13]And in this diagram to the right, we have colored marble example.

[00:08:17]So, it's stacked up. The B stands for blue, the Y stands for yellow, and the G stands for green.

[00:08:24]>> [clears throat] >> So, you can see we have seven marbles.

[00:08:27]So, if they were inside a bag, you would have seven possible outcomes pulling a marble out of the bag.

[00:08:42]You have two blues.

[00:08:47]You have two yellows.

[00:08:52]And you have three greens.

[00:08:58]So, these are our sample spaces right here.

[00:09:02]This is our sample space. We'll call it a list.

[00:09:12]All right, let's go down to the next part. We've talked about all possible outcomes, and now we're going to talk about favorable outcomes.

[00:09:19]If you recall what we talked about in the very beginning of the lesson, our favorable out comes are the X values, and our all possible outcomes are the Y values for our ratios.

[00:09:33]Let's take a look at the favorable outcomes.

[00:09:42]In this, we call it the desired event.

[00:09:51]Here are some examples of simple desired events.

[00:09:57]You can see here in blue it says P, the capital P stands for the probability. So, put a little arrow right here and write down the word probability.

[00:10:12]What's the probability of this event happening? The event will be listed inside these parentheses, and how do you find that? Well, it's a ratio. You can see the fraction bar right here. You have the number of favorable outcomes, which would be X on top, and the number of possible outcomes, the sample space on the bottom, which would be your Y.

[00:10:36]Let's see how easy this is.

[00:10:38]Our first example is a coin.

[00:10:41]Okay, it says the words I want, and that's the event that you're looking for.

[00:10:46]So, in this one it says, "What's the probability of a tails coming up with one flip?"

[00:10:53]Well, how many tails are on a coin?

[00:10:55]There's only one.

[00:10:57]So, you put one. That's what you want to happen, the tails, over the two possible outcomes. There's a heads and a tails, so there's two different things that can happen.

[00:11:08]And so, when you work this out, you can see that a half is equal to 50%.

[00:11:14]And this is a is as likely as not. Let's fit this in here.

[00:11:26]As likely Well, I can't spell. Let me try that again.

[00:11:31]As likely as not.

[00:11:38]Or you might want to say you have an even chance.

[00:11:42]It's a lot to fit in there, so we have to erase and get it dialed in.

[00:11:49]Let's go on to the next one for the coin.

[00:11:51]What's the probability of getting a heads? Well, there's only one heads on a coin, so that's one out of the two sides, the sample space. So, you have a one in two shot. That is also 50 %. That's as likely as not. An even chance, 50/50.

[00:12:09]What about the probability of the coin landing on its edge?

[00:12:13]Well, uh let's just say it's impossible.

[00:12:20]No way of that happening over the two places, so this is a zero % chance of happening.

[00:12:27]And finally, the last one. What's the probability of flipping the coin and getting feet? Well, there are no feet on a coin, so we say zero out of the heads and tails sides. Also a zero %.

[00:12:42]So, that's how it works. You can see the event is inside right here, the favorable outcome. We want tails, we want heads, we want an edge, and we want feet. Let's look at a die, the number cube.

[00:12:58]So, I want the probability What's the probability of rolling a three?

[00:13:02]Well, how many threes are on a die?

[00:13:05]There is only one.

[00:13:06]And how many sides are there? What's the sample space of a die? There are six sides.

[00:13:13]So, if you do 1 / 6 on your calculator, you'll get your percentage.

[00:13:21]1 / 6 is about, rounding, 17 %.

[00:13:32]So, this is highly un- likely.

[00:13:44]The next one, what is the probability of rolling an even number? Well, the even numbers on a die are two, four, and six. So, there are three sides that have an even, so we put a three over the six sides. And 3 / 6 as a percent is 50 %.

[00:14:04]That is as likely as not, or even.

[00:14:10]What's the probability of getting a number greater than one? Well, the numbers that are greater than one are two, three, four, five, and six. So, that's five of the six sides.

[00:14:25]So, we'll do 5 / 6.

[00:14:31]And then we'll multiply that by 100 to make it into a %.

[00:14:37]And it's going to round to 80 %.

[00:14:42]And that is highly likely.

[00:14:52]What's the probability of getting a prime number? Well, from elementary school you learned about prime numbers, and prime numbers mean that you can only have two factors. So, the numbers that have two factors on a die are two, because 1 * 2 is 2, that's the only way you can get two.

[00:15:10]You can do three.

[00:15:12]1 * 3 only has two factors, one and itself. Four is not a prime number.

[00:15:18]Five is a prime number, 1 * 5.

[00:15:25]And six is also not a prime number, so there are three of them of the six sides. And that's another 50% chance.

[00:15:40]Okay, moving on to a card deck.

[00:15:42]I want the probability of a queen of hearts. Now, how many queen of hearts are there in a deck of cards? Well, there's four queens, and one of them is a heart. So, you only have one out of the 52 chance. So, we're going to do 1 / 52 * that by 100.

[00:16:08]And your chances are going to be rounding to 2%.

[00:16:13]That is almost impossible, but it can happen.

[00:16:18]So, we're going to call that highly unlikely.

[00:16:28]Fit it in there, there's not a lot of room.

[00:16:31]What's the probability of getting a red card? Well, the two red cards are hearts, all the hearts and all the diamonds.

[00:16:40]That's half the deck. So, half of 52 is 26. So, you have a 26 in 52 chance of pulling a red card from the deck.

[00:16:52]And if you 26 / 52, you'll get 50 %.

[00:16:59]What's your chances What's the probability of pulling an ace from the deck? Well, how many aces are in a deck of cards? You have four suits, and so you have the ace of hearts, ace of diamonds, ace of clubs, and ace of spades.

[00:17:14]So, here you'll put in four out of 52.

[00:17:22]Put that in your calculator, 4 / 52.

[00:17:26]And times it by 100.

[00:17:29]Round to the nearest percent, and it's going to be about 8%.

[00:17:34]Another highly unlikely draw.

[00:17:38]And finally, the face card. What is a face card? Well, any card that has a face on it.

[00:17:44]So, if we go back up to the list here, these are face cards.

[00:17:49]The jack, the queen, and the king. Well, there are three per suit, and there are four suits, so 4 * 3 is 12 cards.

[00:17:59]12 cards have a face on them.

[00:18:02]So, we'll put 12 out of the 52. So, we'll do 12 / 52 * that by 100.

[00:18:16]And we get about 20 %.

[00:18:21]So, another highly unlikely, but almost unlikely.

[00:18:26]If it had have been 25 or greater, it would have been All right, let's go to the last section here. We have the colored marbles, and we're going to be using uh this example right up here.

[00:18:45]All right. So, what's the chance of drawing a blue marble out of this collection of marbles? Well, there are two of the seven. So, we're going to say two of the seven.

[00:18:58]Turn this into a percent.

[00:19:01]2 / 7.

[00:19:07]And times it by 100.

[00:19:10]And we have rounding to 29 %. So, that is unlikely.

[00:19:21]What about a green? Well, how many greens do we have? We had three of them.

[00:19:26]So, we're going to do 3 sevenths.

[00:19:30]So, 3 / 7.

[00:19:35]* that by 100.

[00:19:38]And we're going to round to 43%.

[00:19:43]So, that is unlikely again.

[00:19:48]What about a red one?

[00:19:50]Well, there are no reds in the bag, so you put zero, cuz that's my favorable. I want red, but there are zero of them in the bag out of seven.

[00:19:58]And that's going to be a 0% and that's said to be impossible.

[00:20:06]And what about a blue or white? So, we have to do some addition here. Blue, there are two of them.

[00:20:13]And white, there is two of them.

[00:20:16]So, add those together, that's a total of four marbles that we would prefer.

[00:20:21]That's what we want. We want blue or yellow. We're not choosy out of the seven.

[00:20:26]And then we'll do 4 / 7 and we're going to multiply that by 100 and we'll get close to 50 7% and that is likely.

[00:20:45]Good chance of that happening.

[00:20:49]All right.

[00:20:50]There you have it. That's what favorable outcomes are.

[00:20:54]Now, as we flip to the backside we're going to be looking at something you might want to say the opposite.

[00:21:03]So, let's write the word complement with quotation marks around it.

[00:21:07]And we might say opposite.

[00:21:18]So, what is the complement?

[00:21:20]The probability of an event not occurring.

[00:21:26]Like we don't want it to happen. That's what the complement is. And how do we know we're looking for a complement?

[00:21:31]This little piece right here, this apostrophe is the notation that you are looking for the complement. That notation means complement.

[00:21:48]What's complement mean?

[00:21:50]The opposite.

[00:21:52]So, this is saying, "What's the probability of this event not happening?"

[00:22:02]You got to be very careful that you see the complement sign here.

[00:22:07]So, let's take a look at the very first one, the coin.

[00:22:10]I want the probability of tails not happening. We do not want it to happen. So, what's not tails on the coin?

[00:22:21]That would be the heads.

[00:22:23]So, the heads, that's what's not tails.

[00:22:26]So, we put heads up here. We want heads to happen.

[00:22:34]Supposed to say heads over the two sides. So, there's only one heads on a coin divided by two and we get 50%.

[00:22:45]Okay, this next one, what's the probability of heads not happening?

[00:22:50]Well, what else is there on a coin?

[00:22:51]There is tails.

[00:22:53]So, we want tails to happen.

[00:22:56]Of the two sides, that's a one in two chance.

[00:23:01]50%.

[00:23:03]What's the probability of feet not happening? Well, what's our choices?

[00:23:09]There is a tail side and there is a head side.

[00:23:13]So, that's two things that can happen.

[00:23:15]Two favorable things, like cuz we don't want the feet to happen out of the two sides. And that is 100%. We have a certain chance of that happening.

[00:23:28]It will happen.

[00:23:30]All right, now that you're getting familiar with the complement and how confusing that can be, let's take a look at the die or a number cube.

[00:23:37]This says, "I want the probability of three not happening."

[00:23:44]Well, what sides on the die are not three? We have a one two four five and six. So, there are Sorry, five sides that are not three.

[00:23:57]So, that's a good chance. We have five sides that we would want cuz we don't want three out of the six sides.

[00:24:05]So, again, we'll go to our calculators and do 5 / 6 and multiply it by 100 to get nearly 80 3%.

[00:24:20]So, this is highly likely.

[00:24:29]Next one, what's the probability of rolling an even not rolling an even, but an an even number not rolling.

[00:24:38]Not rolling.

[00:24:40]Well, what numbers are not evens on the die?

[00:24:44]Well, you have a one a three and a five. So, there are three of the six sides that are not even.

[00:24:51]And that is 50%. A 50/50 shot.

[00:24:56]Remember, that's called even or as likely as not.

[00:25:02]Next one, what's the probability of not a four? But look, it's tricky.

[00:25:08]What's the probability of not a four?

[00:25:10]What not not a four?

[00:25:13]So, let's take this a little slow here.

[00:25:17]What's not a four inside this event?

[00:25:19]What's not a four? Well, that would be a one two three five and six.

[00:25:26]So, if you were looking for how to get a one, two, three, five and six then that would be good, but we don't want that. So, it's not a four, but we want the complement of this. So, what's the opposite of one, two, three, four or sorry, one, two, three, five and six? A four.

[00:25:46]It's confusing, but that's the answer.

[00:25:48]That's a one in six shot.

[00:25:52]So, we do 1 / 6 and we get 17% nearly. Rounding to the greatest or the whole percent.

[00:26:06]That one was a tricky one.

[00:26:09]The next one is a card deck.

[00:26:13]I want the probability of the queen of hearts not to happen. So, I'll be happy with any other card in the deck. I just do not want the queen of hearts.

[00:26:23]So, there is only one queen of hearts and that means out of 52 cards, there are 51 cards 51 cards of the 52 in the deck.

[00:26:37]So, 51 / 52 times it by 100 and it is nearly 98% chance happening.

[00:26:47]Super high.

[00:26:49]Super high.

[00:26:52]Highly likely.

[00:27:00]What about the probability of a black card not being drawn?

[00:27:06]Well, the black cards are the clubs and the spades.

[00:27:18]Okay, so we don't want a black card drawn. So, we would be happy with the red cards and that would be hearts and diamonds.

[00:27:28]That splits the card deck in half and half of 52 would be 26 red cards out of the 52.

[00:27:38]And that's going to be 50 percent chance.

[00:27:42]And finally, for the deck deck of cards, what's the probability of getting a two through five? So, that's two three four or five.

[00:27:55]And that's in the four suits, hearts diamonds uh clubs and spades.

[00:28:09]Super tiny.

[00:28:11]All right. So, how many cards is that?

[00:28:14]Well, let's take a look.

[00:28:16]We have one, two, three, four cards right here.

[00:28:20]And there are four suits, so 4 * 4 is 16.

[00:28:24]All right, now 16 is what you want not to happen. So, what do you want to happen? So, we don't want these cards. What's the opposite of it?

[00:28:33]Well, if there's 16 cards, let's do some math here. 52 - 16 That means there's 36 cards that are not these. So, we'll put 36 over 52.

[00:28:53]36 / 52 is nearly 69%.

[00:29:03]And the last section here, we have colored marbles.

[00:29:07]And remember, always be looking for the complement right here. If you don't see them, write them in because all of these right here in this section are working on the complement. Okay, so that's what this whole table is supposed to be. So, every one of these should have the complement sign. So, make sure that you can see them.

[00:29:29]Let's go ahead and move through it.

[00:29:31]What's the probability I want the probability of blue not to happen?

[00:29:38]Okay, so in the bag, you saw that there was two yellows and there were three greens and two blues. So, we don't want the two blues, but we we would take a yellow or a green. So, two and three is five. So, you have a five in seven chance or seven marbles in the bag.

[00:29:59]So, on that we'll just do five divided by seven times it by 100 and it's nearly 71% chance.

[00:30:17]So, that is likely.

[00:30:22]What's the probability of green not to happen?

[00:30:26]Well, green has three. We would gladly take a yellow or a blue and that would be four out of seven chance and four divided by seven is going to be nearly 57%.

[00:30:42]And finally, this last one. What's the probability of red not to happen? Well, there are no reds in here, so you would gladly take a yellow, green, or blue.

[00:30:51]So, add up all those, which would be seven out of seven and that is 100% chance.

[00:30:57]And that is said to be certain.

[00:31:04]All right. So, now you've learned all about favorable outcomes.

[00:31:13]The favorables over the all possibles.

[00:31:22]And you've also learned about the complement.

[00:31:25]The non-favorable.

[00:31:27]The opposite of what you want. And you're looking for this special sign right here.

[00:31:33]The complement.

[00:31:39]Okay, we're going to come down into your check your understanding. Always go back up and use all of your notes to help you through this section down here.

[00:31:49]We're going to run it the same way as we have been.

[00:31:52]And you are going to start down here as a class >> [snorts] >> and do example one.

[00:31:58]Let's take a look at this.

[00:32:01]Example one on quadrant one.

[00:32:03]Find the probability of randomly picking a white marble as a ratio, a decimal and a percent. So, if we look in the bag here, you can see that there are one two three four white marbles.

[00:32:23]Okay, and how many marbles are there total?

[00:32:26]Well, there are two black ones and there are uh four, let's call those zebra ones.

[00:32:32]Okay? So, we have the four white ones.

[00:32:36]We have the two black ones and we have the four zebra ones. And we're going to add up all those and we're going to get 10.

[00:32:44]All right, there are 10 total marbles inside this bag.

[00:32:48]So, let's make a ratio. Find the probability of randomly picking a white marble. So, if we wrote this correctly, it would be the probability of drawing a white marble.

[00:33:03]Okay, so what does that look like as a ratio?

[00:33:06]Well, a ratio can be written three different ways based on the top of your notes. And one way would be four out of 10.

[00:33:17]Another way would be four out of 10.

[00:33:21]And the last way would be four to 10. So, those are all ways you can write it as a ratio.

[00:33:30]As a decimal, you just take this fraction right here and you divide it.

[00:33:34]Four divided by 10 and you get 4/10.

[00:33:44]As a percent, you just multiply your decimal by 100.

[00:33:49]And 100 * 4/10 on your calculator is 40.

[00:33:56]Now, a percent can't be a percent without the sign. So, make sure you include the percent sign.

[00:34:02]So, there you have it. That's your example one of the probability of drawing a white marble out.

[00:34:10]Now, it's time to go back to the mild, medium, and spicy. This is when you pick your problem that you want to try.

[00:34:17]Um mediums are most like the test.

[00:34:25]Okay?

[00:34:26]Um you pick on this first row if you're going to do the mild, the medium, or the spicy. Pause now and do this in example two space.

[00:34:45]All right, you're back and I'm not sure which one you chose, the mild, medium, or spicy.

[00:34:50]But we're going to start with the first medium right up here.

[00:34:55]So, let's take a look at this before you go on to your example three.

[00:34:59]It says a deck of 20 cards and these 20 cards are labeled 1 through 20. So, they're not playing cards, they're just regular cards with numbers on them.

[00:35:10]One card is drawn. So, that's very important to see it's one card because that is a simple event.

[00:35:17]Which statements are true?

[00:35:19]An even card is certain.

[00:35:21]Well, how many even cards are there in 1 to 20? That'd be half of them. So, that'd be a 10 in 20 chance. Well, to be certain, it'd have to be 100% and that is not okay. So, that's bad deal there.

[00:35:37]Not true.

[00:35:39]Moving on to the next one.

[00:35:41]Let's put uh let's put certain is supposed to be 100%.

[00:35:45]And this turned out to be 50%.

[00:35:48]That's why that is no good.

[00:35:51]The next one, likely for a number greater than 10.

[00:35:55]Okay? So, the word likely, that means above 50%.

[00:36:00]So, do we have a above 50%? It says for a number greater than 10. That would be 11 to 20. So, how many cards is that?

[00:36:08]11 12, 13, 14, 15, 16, 17, 18, 19 20.

[00:36:17]Well, that looks like to be 10 cards.

[00:36:26]10 divided by 20 again is 50% and that's as likely as not. This is the word likely. So, this is another false statement. So, we'll put a false in the first one a false in the second one.

[00:36:40]The next one unlikely to pick cards 1 through 9.

[00:36:45]So, 1 through 9 how many cards is that? That's nine cards.

[00:36:52]So, let's put 9 over 20.

[00:37:00]And then put that in our calculators.

[00:37:01]Nine divided by 20 is 45%.

[00:37:11]And 45% is unlikely. So, this is our first true statement.

[00:37:18]Card 26 is impossible.

[00:37:21]Well, how many 26 How many cards are labeled 26? There are zero out of the 20 and that is 0% which is impossible. That's another true statement.

[00:37:34]And the last one, unlikely to draw a double digit card.

[00:37:40]Okay, well, how many double digit cards are there?

[00:37:44]Well, there's the number 10. So, we're going to count them.

[00:37:47]10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20. There are 11 of them out of the 20. And 11 divided by 20 is 55%.

[00:38:06]That's likely.

[00:38:07]It says the word unlikely. So, this is a false statement. So, there were only true two truths.

[00:38:14]The third and fourth one.

[00:38:16]All right, now that we did that one you may or not may not have chosen that one for your example two.

[00:38:23]Um you're going to pause the video and try example three.

[00:38:28]And when you come back I'll have answers for all of them.

[00:38:35]Pause now.

[00:38:42]Okay, we're back and I've done a lot of them except for the last medium one.

[00:38:46]Let's take a look at these just in case you did one of these for your uh third one. So, the mild over here you can see the answers to be It said list them in both decimals and percents. And so, we have 125 thousandths, 12.5%.

[00:39:06]625 thousandths, 6.25 hundredths percent.

[00:39:12]Five tenths and 50%.

[00:39:15]Moving down to the last mild for the soccer one for the probability of getting a C, there are two Cs out of the six letters.

[00:39:23]That's a 33% chance.

[00:39:26]What's the probability of not getting a vowel? There's the not sign right there.

[00:39:30]There are four letters that are not vowels. That'd be S, C, and R. That's four out of six, 67%.

[00:39:37]And what's the probability of drawing out a B? Well, there are no bees, so that is a 0%.

[00:39:44]Sliding all the way over to the spicy problems.

[00:39:49]We got a story about Clovis Crush giving away t-shirts.

[00:39:53]And we're looking for true statements.

[00:39:55]The first one is, it is likely to receive your perfect fit. Well, my perfect fit is an XL, so I did 12 / 57 and I got less than 50%, and so that is unlikely that I would get my choice. So, that's a false statement for me. And because they're all 9, 14, 21, 12, and 1, it wouldn't matter what size you chose, it would have been false. Cuz it it is not likely.

[00:40:24]The next one, uh Eli wears a small or medium. Unlikely pick. Well, he'll choose a small or a medium, so the smalls and the mediums combined are 23 / 57, which is 40%, and that is unlikely, and that is a true statement.

[00:40:41]Jack wears large, likely to get one.

[00:40:43]Well, there are 21 of them out of the 57, that's 37%, and that is not likely.

[00:40:48]That's false statement. And Clovis Crush gave away all the shirts. About half received a large. Well, there were 21 larges out of the 57, that's a 37% chance, and that is not I would not consider that about half. So, that's another false statement.

[00:41:06]Moving down to the last spicy one. In a deck of cards, find the probability of following. The probability of a queen or a six. Now, be careful cuz there are four queens, but one of those um or a six. Okay, sorry. A queen or a six.

[00:41:22]So, the I do have an error here. I do want to fix that. That's an eight.

[00:41:28]An eight out of 52 chance.

[00:41:35]So, 8 / 52 is 15%.

[00:41:43]Okay, caught that error. The next one is, what's the probability of getting an ace, a 10, or a black card? Now, be careful because one or two of the 10s are black and two of them are reds, and two of the aces are black and two of them are reds. So, the black cards would be 26 of them, that's half the deck, plus you got two more 10s, and you got two more aces. That's four more cards there. That's two here, two reds, two reds, and 26 of these. And I have another error. That's supposed to be 30.

[00:42:18]Good thing I'm going over these again.

[00:42:22]So, 30 / 52 and that's going to be nearly 58%.

[00:42:33]Let's see if I made made an error on this next one. What's the probability of getting a queen or a six, but not those. It's the complement. And I do make another error here.

[00:42:46]Math was certainly off as I was doing this one.

[00:42:51]So, there are total eight, so we don't want this first one to happen, so the opposite of eight or 52 - 8 would be 40 four out of 52. So, let's do 44 / 52.

[00:43:12]It's going to be nearly 85%.

[00:43:18]Okay, let's see if I did this one right.

[00:43:20]What's the probability of getting a red card or a face card not to happen? Okay?

[00:43:25]So, a red card or a face card. So, how many red cards are there? There are 26 of them.

[00:43:31]Or a face card.

[00:43:33]Uh well, how many of the red cards are face cards? There are Let's say, how many face cards are there? There are 12 of them cuz there are four in each Sorry, three in each suit * four suits, that's 12. Well, half of those would be red, which we already have them accounted for, and half of them would be black.

[00:43:50]So, what's the half of 12? It would be six. So, 12 + 6 is 32.

[00:43:57]And then we have to find the opposite of 32. So, 32 or 52 - 32 would be 20, and I did get this one right. It is 38%.

[00:44:07]And the last one, the probability of a card with two eyes. So, this one you got to really know your deck. Have you ever heard the expression the one-eyed jack?

[00:44:18]That's because the jack card you can only see one eye on the jack. The kings and the queens, you can see both their eyes, and so there are eight of these out of 52, which is 15%.

[00:44:31]I know those are all correct now. So, let's go on to the last one that you may or may not have done yet. It's the middle medium problem.

[00:44:41]List each as impossible, unlikely, impossible, unlikely, as likely as not, or likely, or certain.

[00:44:54]Okay, there's That was a little bit confusing, wasn't it?

[00:44:58]Yeah, it was. Let's Let's get these impossible, certain.

[00:45:03]So, remember, impossible is 0%.

[00:45:07]Certain is 100%.

[00:45:10]As likely as not, right here, is 50% exactly.

[00:45:17]And then, we'll change our colors here. We have likely and we have unlikely.

[00:45:23]Remember, unlikely is anywhere from between 0% not 0%, but between 0% all the way up between 50%, but not 50.

[00:45:37]And then likely is going to be 50 up to 100. All right, let's go ahead and start. What's the probability of rolling an even number? So, we're using a number cube. That's a three in six chance, that is 50 percent, and we're supposed to label it.

[00:45:59]That is as likely as not.

[00:46:03]As likely as not.

[00:46:11]The next one here, we have the probability of two, three, five, or six.

[00:46:16]>> [clears throat] >> So, on a number cube, there are those four numbers.

[00:46:20]So, 4 / 6 is going to give us a 67%.

[00:46:26]percent.

[00:46:27]And that right there is likely.

[00:46:35]The next one is a four or a six. There are two possibilities there, two out of the six.

[00:46:41]That's going to give us a 33%.

[00:46:45]That is unlikely.

[00:46:52]And then the probability of getting a number greater than six, those are impossible cuz that would be a seven or an eight. There are zero of them.

[00:47:02]That's 0%, which is impossible.

[00:47:08]And the probability of getting a number not a number. Is it possible to roll a die and not get a side?

[00:47:15]Absolutely not.

[00:47:17]So, it's another zero out of six, which is 0%, and that is im- possible.

[00:47:32]All right, going on down to close off your examples down here, you want to stop and take a look at this one. Things to remember.

[00:47:41]I think that you ought to put down the difference between favorables and complements.

[00:47:47]So, favorable and complement.

[00:47:53]Favorable is the event that you want to happen over the what?

[00:48:00]Sample space.

[00:48:03]You might want to write sample space all the way down here.

[00:48:06]Or you might want to write the I want over all the possibles. However it is that you're going to remember it best. Makes sense to you.

[00:48:20]The complement is what you want not to happen out of the sample space.

[00:48:27]And remember, you might want to write down P and that this is the event.

[00:48:35]And what does P mean?

[00:48:37]It means the probability.

[00:48:42]And how do you do this?

[00:48:43]You do the favorables of all possible outcomes.

[00:48:48]So, write down even more, whatever you need to do.