Assignment:
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.
Provide complete and step by step solution for the question and show calculations and use formulas.