Jim is considering pursuing an MS in Information Systems deg

Jim is considering pursuing an MS in Information Systems degree. He has applied to two different universities. The acceptance rate for applicants with similar qualifications is 20% for University X and 45% for University Y. What is the probability that Jim will not be accepted at either university?

.30
.36

.44

or .56?

Solution

Given P(X) = 20% = 0.2; P(Y) = 45% =0.45

Assume acceptance by universities are independent

so P(X and Y ) = P(A) P(B) = 0.2*0.45 = 0.09

Probability that jim will not selected either university = 1- P(A or B) = 1- P(A)-P(B) + P(A and B)

= 1- 0.2-0.45+0.09 = 0.44