### Video Transcript

Okay, so he was trying to figure out we flip a fair coin, the number of flips that would be attained, he said. A number of flips that would be obtained either until two tails are achieved or until the coin has been flipped six times. It ‘s well literature xB the number of queen flips. And then nowadays, bazaar coin. The probability of getting a heads is peer to the probability of getting eight Hales, which is 1/2. sol do n’t do this in stages, right, because we do n’t have excessively many cases to look at. The number of folks is a minimum of two, and it goes up to six. So we ‘ll look at what happens when x equals two when adam equals 345 and six and then to get out from there. So the beginning case, it ‘s gon sodium be the probability of when X is equal to two eso This assumes and that our 1st 2 flips for both tails and that occurs with the probability of it entails times the probability of getting tails. Or we could just square it. This would be 1/2 times 1/2 or point 25 Okay, so then The second case is going to be where we have three coin flips. And then the thing is, in this exemplify, we know the third base football details. But one of the 1st 2 is the heads. The order does not matter. And since order does n’t matter, we will use a combination. So a combination, uh, to choose one because we ‘re choosing one of the 1st 2 to be heads multiplying that, you know that there are in these three flips there ‘s two tails. So the probability of tales times credibly tails and there is one head, so we want to multiply it by the probability of getting heads. You ‘ll see that the experience here there is a two and a one is equal to the number of flips, right ? Yes. Once we types that into our calculator but ends up being to choose one. This these problems are the lapp. It ‘s actually getting 10.5 to the third base. Karen ‘s gon na be equal to 0.25 master a new page here. then for the probability that we have four flips, he ‘s gon na follow this same rule. We ‘re gon na have to choose a combination again or is n’t matter. But two of the 1st 3 foots were heads or choosing to from three to be our heads. Two of these four is going details. We ‘re stopping at two tails. Okay, so you want the probability of Tales Square ? But the other two are going to be heads very wanted ticket, probably a head squid. And again you see the exponents two and two is equal to four that this will be peer to three Choose to That was 1/2 to the fourthly and this ends up being adequate to we put it in the calculator 0.187 five. So there ‘s two more cases. Nest is where we have five flips and following the same routine in so far choosing three from Forbes. We ‘re choosing three of the beginning four flips to be heads, knowing that the 5th 1 was tails And then since we have two tails will multiply that by the problem of getting entails squared. But then we besides have three heads. indeed I want to point out that it credibly getting our heads three times. Where to the one-third baron ? Yes, this is it being for choose three times 1/2 to the fifth, which is equal to point 12 five. Yes, and we have one case left to look at. And that ‘s going to be where we have six flips, right ? so careless of what happens on the one-sixth flick, we start flipping. Okay, but four or five of the 1st 5 flips has to contain heads. Eso basically there could be at most one. And so besides embrace that we have to add these two cases together. So we have the encase where we ‘re choosing five. Choose four with one has one tail and the foreheads. Or there ‘s the casing we ‘re choosing 55 Where ‘s all heads and no Kale ‘s. Okay, so there ‘s either case, whether it was one dock merely this inaugural part or the font where there was no tales in the second partially. And so we add that up in concert. so get five shoes for okay times 1/2 to the fifth and leaving it at that to five. Choose five, 1/2 to the fifth. And, of course, whether the last one is tails or not, we are stopping. So it it is a relevant all right, and this is adequate to 0.18 seven fine and cement. We figured out the weapon for each case, we can move on to find the expect measure. Okay, so the expect value then is going to be equal to the count off each. Tom had tails occurrence times the probability of that currents. indeed when we have the lawsuit where adam is equal to two for two flips, that probability was, uh, 0.25 I ca n’t allow that to. When we had three flips thin, the probability was besides 0.25 for four flips got more interesting. It was 0.1. Eat 75 for five. Flips are probability was 0.1 to five. And then, last, to get six flips, probably of that occurring was 60.18 75 Okay, so once we add all that up, we ‘ll find that the ask value is about three bespeak 75 So you ‘d expect to get between three and four flips to get your two tails, but closer to four

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