Jane is a better tennis player than Jack.If the probability that Jane will beat Jack in any given game is 0.7, what is the probability that they will each win one game if they play two games? (Note that there are two ways they can arrive at this outcome: Jane wins the first game or Jack wins the first game.)
A) 0.21
B) 0.3
C) 0.42
D) 0.6
E) 1

Question

Quizplus · Accepted Answer

There are four possible outcomes for the two games: JJ, JJ, JJ, and JJ.

The probability that they will each win one game if they play two games is the sum of the probabilities of the first and second outcomes:

P(JW, JW) + P(JL, LJ)

= P(JW)P(JL) + P(JL)P(JW)

= 0.7(1-0.7) + (1-0.7)0.7

= 0.42

Therefore, the answer is Choice C.

Jane Is a Better Tennis Player Than Jack