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82 if you pick a random contestant what is the

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8.2 If you pick a random contestant, what is the probability that she isallowed to stay during both of the first two episodes?
8.3 If you pick random contestant who was allowed to stay during the firstepisode, what is the probability that she gets kicked off during the secondepisode?
4
CS182 HW69. (BONUS 20 points) Some games, like tennis or ping pong, reach astate called deuce. This means that the score is tied and a player winsthe game when they get two points ahead of the other player. Supposethe probability that you win a point is p and this is true independentlyfor all points. If the game is at deuce what is the probability you winthe game?LetWbe the event you win the game from deuce andLthe event you lose. For conveniencewe definew=P(W).The figure shows the complete game tree through 2 points.In the third level we justabreviate by indicating the probability of wining from deuce.The nodes marked +1 and-1 indicate whether you won or lost the first point.Summing all the paths toWwe getw=P(W) =p2+p(1-p)w+ (1-p)pw=p2+ 2p(1-p)ww=p21-2p(1-p)5
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W.Szpankowski

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