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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 _______________
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