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# Probability

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.
1) _______________

2. Find the probability that the tournament lasts exactly 3 games.
2) _______________

3. Find the probability that the tournament lasts exactly 4 games.
3) _______________

4. Find the probability that Fran wins the tournament.
4) _______________

5. Find the probability that the tournament lasts exactly 3 games if it is won by Fran.
5) _______________

6. Find the probability that Fran won the tournament if it lasted exactly 3 games.
6) _______________

#### Solution Preview

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 ...

#### Solution Summary

This solution is comprised of detailed explanation and step-by-step calculation of the given problem and provides students with a clear perspective of the underlying concepts.

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