Assume you have applied to two different universities (let\'srefer to them as Un

Question

Assume you have applied to two different universities (let'srefer to them as Universities A and B) for your graduatework. In the past, 25% of students (with similar credentialsas yours) who applied to University A were accepted, whileUniversity B accepted 35% of the applicants. Assume events areindependent of each other.

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

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

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

           d.   What is the probability that neither university willaccept you?

Explanation / Answer

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

P(A and B)=P(A)*P(B) (Since Assume events areindependent of each other)

=0.25*0.35

= 0.0875

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

P(A or B) = P(A) +P(B)- P(A andB)

=0.25+0.35-0.25*0.35

=0.5125

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

P(A and B') + P(A' and B) = [P(A)-P(A and B)]+ [P(B)-P(A and B)]

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

=0.425

           d.   What is the probability that neither university willaccept you?

P(A or B)' = 1-P(A or B)=1-0.5125=0.4875

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.