The probability that team A will not win the tournament is

Roland2rule 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 = 0.2

The probability that team B will NOT win the tournament is 60%
So P(team B WILL win the tournament) = 1 - 0.6 = 0.4

If 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

BTGmoderatorRO 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%

Recall that P(A or B) = P(A) + P(B) - P(A and B). The probability that team A wins is 1 - 0.8 = 0.2 and the probability that team B wins is 1 - 0.6 = 0.4. Since they can’t both be the winner, P(A and B) = 0. Thus,

P(A or B) = 0.2 + 0.4 - 0 = 0.6

Answer: D