You applied to two different universities (A and B) for your graduate work. In t

Question

You applied to two different 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?

Thank you for the help, I do not understand this sample question. How do you find the probability of each event independently?

Explanation / Answer

Given P(A)=0.25 Let P(A') be the probability that you will not be accepted by university A P(B) = 0.35 Let P(B') be the probability that you will not be accepted by university B Assume events are independent of each other. a.What is the probability that you will be accepted in both universities? P(A and B) = P(A)*P(B)=0.25*0.35 = 0.0875 b.What is the probability that you will be accepted to at least one graduate program? P(A or B) = P(A) +P(B) -P(A and B) = 0.25 +0.35 - 0.0875 = 0.5125 c.What is the probability that one and only one of the universities will accept you? P(A and B') + P(A' and B) =P(A) - P(A and B) + P(B) - P(A and B) =0.25 - 0.0875 + 0.35 -0.0875 =0.425 d.What is the probability that neither university will accept you? P(A' and B') = P(A')*P(B') = (1-0.25)*(1-0.35) =0.4875

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