Suppose Donald and Hillary play a series of games in which t

Suppose Donald and Hillary play a series of games, in which the probability that Hillary wins any particular game is 0.6. Whoever wins 6 games wins the series.

(a) What is the probability that Donald wins after 8 games?

(b) What is the probability that the series comes down to a final game whose winner determines the winner of the series (analogous to a final, 7th game for the world series)?

(c) If the series is in the eighth game, with Donald at 4 games and Hillary at 3, what is the probability that Hillary \"sweeps\" by winning the next three games?

Solution

Suppose Donald and Hillary play a series of games, in which the probability that Hillary wins any particular game is 0.6. Whoever wins 6 games wins the series.

(a)The probability that Donald wins after 8 games is:

0.6^6*0.4^2=0.0074

(b)The probability that the series comes down to a final game whose winner determines the winner of the series is:

0.6^6*0.4=0.018

(c) If the series is in the eighth game, with Donald at 4 games and Hillary at 3, then the probability that Hillary \"sweeps\" by winning the next three games is:

0.6^6*0.4^2+0.6^2*0.4^6=0.371