A B 3 3 6 P A B 4 2 6 Therefore by Bayes rule P B 4 A 2 6 1 45 6 1 4 4 6 1 4 3

# A b 3 3 6 p a b 4 2 6 therefore by bayes rule p b 4 a

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(c) If they play the game for 5 rounds, what is the probability that Alice wins at least 3rounds? (d) If they play the game for 100 rounds, what is the probability that Alice wins at most60 rounds? (Use appropriate approximations.)
4.(20pts) Suppose Alice and Bob are playing with the same dice as in Problem 3 (Alicewith a 6-sided die and Bob with a 4-sided die), but the game rule has changed. In eachround they both roll their dice. Whoever gets the first ace is the winner of the game. Ifthey both get aces in the same round, then it is a draw.(a) Suppose they keep on rolling the dice until each of them get their own first ace. LetXandYbe the numbers of rounds required for Alice and Bob to get her and his firstace, respectively. What is the distribution ofXand what is the distribution ofY?

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