Assume you have applied to two different universities (let\'s refer to them as U

Question

Assume you have applied to two different universities (let's refer to them as Universities A and B) for your graduate work. In the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are independent of each other.

a. What is the probability that you will be accepted in both universities?

b. What is the probability that you will be accepted to at least one graduate program?

c. What is the probability that one and only one of the universities will accept you?

d. What is the probability that neither university will accept you?

Explanation / Answer

n the past, 25% of students (with similar credentials as yours) who applied to University A were accepted, while University B accepted 35% of the applicants. Assume events are...

Probability that University A will Accept = 0.25

Probability that University A will Reject = 1- Probability that University A will Accept = 1- 0.25 = 0.75

Probability that University B will Accept = 0.35

Probability that University B will Reject = 1- Probability that University B will Accept = 1- 0.35 = 0.65

a. What is the probability that you will be accepted in both universities?

= 0.25 * 0.35 = 0.0875   = 8.75 %

b. What is the probability that you will be accepted to at least one graduate program?

1 - Probability that none will accpet : 1- ((1-0.25) * (1-0.35)) = 0.5125 = 51.25 %

c. What is the probability that one and only one of the universities will accept you?

Prob that A accepted while B rejected + Prob that B accepted while a rejected

0.25 * 0.65 + 0.35* 0.75 = 0.425 = 42.5 %

d. What is the probability that neither university will accept you?

0.75 * 0.65 = 0.4875 = 48.75 %

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