Question

If 36 percent of bureaucrats are in the Defense Department, 25 percent are in the Postal Service, 39 percent are in other agencies, and all agencies are mutually exclusive, what is the probability that a person randomly chosen is in the Postal Service and the Defense Department?

Answer 1

There is some problem in the question framing probably.

If it is asking the probability of person in Postral Service and Defense department separately then fine -

Probability of person in Postal service = 0.25

and probability of person in Defense department = 0.36

Otherwise, if it is asking the probabilities of both together, then it will be zero because the agencies are mutually exclusive.

It is possible that it wanted to ask the probability of person chosen in Postal Service or Defense department in which case - the probabilities of both will be added

i.e 0.25 + 0.36 = 0.61