1. [20pts] Andrew is playing chess with his sister Liz. Andrew may win with prob

Question

1. [20pts] Andrew is playing chess with his sister Liz. Andrew may win with probability 0.6 (assuming independence and the same probability of winning for each game). a) What is the probability that Andrew has won four times if they have played 7 games? b) What is the probability that Andrew have played at most 3 games to win for the first time? ) If Liz refuses to stop until she beats Andrew 3 times (in total, not necessarily in a row), ow likely will they stop playing as soon as they finish the 7th game? 1:11c, lhe NAME ofeach distribution l Topts Amon N sSB keys, 3 of them are defective. You are allowed to take two t without replacement ot be the number of defective ones you took. NAME this dstributionDetermine the PAI for the random variable X. Plot the PME

Explanation / Answer

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1) a)

P = 0.6

P(X = 4) =7C4 * 0.6^4 * 0.4^3

P = 0.29

b) P(X 3)

P = P(X = 1) + P(X = 2) + P(X = 3)

P = 0.6 + 0.4 * 0.6 + 0.4^2 * 0.6

P = 0.936

c) This means 7th game is won by Liz

In remaining 6 games she won 2 times

P = 6C2 * 0.4^2 * 0.6^4

P = 0.31

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