A preparation exam is offered at the Maryville University in St. Louis twice a y

Question

A preparation exam is offered at the Maryville University in St. Louis twice a year for all students who decide to take an actuarial exam of SOA (Society of Actuarials). It is estimated that if a student takes the preparation exam then he or she will pass the actuarial exam with probability 45%. Without taking the preparation exam, the probability of passing the actuarial exam is 15%. In a particular semester, 60% of all students taking the actuaril exam participated in the preparation exam. If a student is randomly selected from the group of students who took the actuarial exam, what is the probability that he or she will pass the actuarial exam? if a student did fail the exam, what is the chance that he or she did participate in the preparation exam?

Explanation / Answer

Let

P = prepares
A = passes the exam

Hence,

P(A|P) = 0.45
P(A|P') = 0.15
P(P) = 0.60

hence,

a)

P(A) = P(P) P(A|P) + P(P') P(A|P') = 0.60*0.45 + (1-0.60)*0.15 = 0.33 [ANSWER]

*************************************************

b)

As

P(A') = 1 - P(A) = 0.67

Then

P(P|A') = P(P) P(A'|P)/P(A') = 0.60*(1-0.45)/0.67 = 0.492537313 [ANSWER]

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