4. (12 points) Assume you have applied to two different universities (Universiti

Question

4. (12 points) Assume you have applied to two different universities (Universities A and B) for getting an MBA degree. In the past, 25% of students 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

a)P(getting accepted in both university) =P(selected in A)*P(selected in B) =0.25*0.35=0.0875

b)P(getting accepted in at least one) =1-P(not selected in A)*P(not selected in B) =1-(1-0.25)*(1-0.35)=0.5125

c)P(one and only one will accept) ==P(selected in A)*P(not selected in B)+P(not selected in A)*P( selected in B)

=0.25*(1-0.35)+(1-0.25)*0.35 =0.425

d)

P(neither university accept you) =P(not selected in A)*P(not selected in B) =(1-0.25)*(1-0.35)=0.4875

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