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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