4. [2.5 points] Consider the set of sequences of five letters chosen from W and

Question

4. [2.5 points] Consider the set of sequences of five letters chosen from W and L. We may think of these sequences as representing the outcomes of a match of five games, where W means the first team wins the game and L means the second team wins the game. Consider a "best of five" match, in other words the match is over when either of the teams has their third win (and the team with three wins is the match winner Thus, some games may never get played, but we need to include their hypothetical outcomes in the points in order that we have a probability space of equally likely points). Assume the games are independent What is the probability that a team will win the match, given that it has won the first game? Indicate your reasoning as well as showing your calculations and formulas

Explanation / Answer

Answer:

probability that team will win the match given won first match =P(won next 3 matches+won 2 out of next 3matches and then won 5th match+won 2 out of next 4matches and then won 6th match+won 2 out of next 5matches and then won 7th match)

=(1/2)3+ + + =0.65625

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