Bunuel wrote:

The probability that team A will not win the tournament is 80% and the probability that team B will not win the tournament is 60%. If there is only one tournament winner, what is the probability that either team A or team B wins the tournament?

(A) 20%

(B) 40%

(C) 48%

(D) 60%

(E) 80%

The probability that team A will NOT win the tournament is 80%In other words, the probability that team A will NOT win the tournament is 0.8

So P(team A WILL win the tournament) = 1 - 0.8 =

0.2The probability that team B will NOT win the tournament is 60%So P(team B WILL win the tournament) = 1 - 0.6 =

0.4If there is only one tournament winner, what is the probability that either team A or team B wins the tournament?This is an OR probability. So, we'll

apply the OR probability formula:

P(event X occurs OR event Y occurs ) = P(X occurs ) + P(Y occurs ) - P(X and Y BOTH occur)So, we get: P(A or B wins tournament) = P(A wins tournament) + P(B wins tournament) - P(A AND B both win tournament)

=

0.2 +

0.4 - 0

= 0.6

Answer: D

ASIDE: P(A AND B both win tournament) = 0, because we are told that "there is only one tournament winner." So, both teams cannot win.

Cheers,

Brent

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Brent Hanneson – GMATPrepNow.com