Question

For one community, the probability that a married man is a college graduate is 35%, the probability that the wife is a college graduate is 41%, and the probability that both the husband and the wife are college graduates is 14%. If a married couple from this community is randomly selected, what is the probability that either the man or his wife is a college graduate? (Write your answer as a percentage.)

A. 62%
B. 70%
C. 76%
D. 80%

Answer 1

The probability that either the man or his wife is a college graduate is 76%.

Step-by-step explanation:

To find the probability that either the man or his wife is a college graduate, we can use the principle of inclusion-exclusion. We start by adding the probabilities of the man and the wife being college graduates, which is 35% + 41% = 76%. However, we have double-counted the probability that both the husband and the wife are college graduates, which is 14%. So, we subtract this double-counted probability once to get the final probability.

P(probability that either the man or his wife is a college graduate) = P(man is a college graduate) + P(wife is a college graduate) - P(both husband and wife are college graduates)

= 35% + 41% - 14% = 76%

Therefore, the probability that either the man or his wife is a college graduate is 76%.