Question

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

Answer 1

Answer:

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) $\times$ (1 - P(B))] + [P(B) $\times$ (1 - P(A))]

=  (0.25 $\times$ 0.60) + (0.40 $\times$ 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.