When John and Carl play a game,John wins,on average,2 out of every 5 games played.Today they agree to play until John wins one game or until three games have been played,whichever comes first.What is the probability that John wins one game today?
A)0.432
B)0.480
C)0.720
D)0.784

Question

Quizplus · Accepted Answer

John's probability of winning any given game is 2/5, and the probability of losing any given game is 3/5. The probability that John wins at least one game today can be calculated by subtracting the probability of him losing all games (if they play three games) from 1. The probability of losing three games in a row is (3/5)^3 = 27/125. Therefore, the probability of winning at least one game is 1 - 27/125 = 98/125 = 0.784.

When John and Carl Play a Game,John Wins,on Average,2 Out