Joe is considering pursuing an MBA degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B. What is the probability that Joe will be accepted at one, and only one, university

The probability that Joe will be accepted at one, and only one, university is 0.45 or 45%.

Step-by-step explanation:

We are given that Joe is considering pursuing an MBA degree. He has applied to two different universities.

The acceptance rate for applicants with similar qualifications is 25 percent for University A and 40 percent for University B.

Let the probability that Joe will be accepted for University A = P(A) = 0.25

Probability that Joe will be accepted for University B = P(B) = 0.40

Now, Probability that Joe will be accepted at one, and only one, university is given by ;

Accepted for University A but not for University B + Accepted for University B but not for University A

=  [P(A) (1 - P(B))] + [P(B) (1 - P(A))]

=  (0.25 0.60) + (0.40 0.75)

=  0.15 + 0.30 = 0.45

Hence, the probability that Joe will be accepted at one, and only one, university is 0.45.