Fran and Ron play a series of independent games. Fran's probability of winning any particular game is 0.6 (and Ron's probability of winning is therefore 0.4). Suppose that they play a best-of-5 tournament. (That is, the winner of the tournament is the first person to win 3 games.)
1. Find the probability that Fran wins the tournament in 3 games.
2. Find the probability that the tournament lasts exactly 3 games.
3. Find the probability that the tournament lasts exactly 4 games.
4. Find the probability that Fran wins the tournament.
5. Find the probability that the tournament lasts exactly 3 games if it is won by Fran.
6. Find the probability that Fran won the tournament if it lasted exactly 3 games.
Dear student, please refer to the attachment for the solutions. Thank You.
Probability of Fran's winning the game = 0.6
Probability of Ron's winning the game = 0.4
1. Required Probability = [(5C3)[ (0.6)3x(0.4)2]
2. The tournament will last exactly three games if either Fran or Ron wins all the first three games.
A: Fran wins the ...
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