Twenty-eight percentof all people who take college statistics classes claim that they found a use for the class sometime during their college career.Of those who found a use for the class, 93% found gainful employment after graduation.Eighty-six percent of all people who take college statistics found gainful employment after graduation.What is the probability that a randomly selected student who took college statistics found a use for the class and found gainful employment after graduation?

Question

Quizplus · Accepted Answer

Let's use the formula for conditional probability:
P(A|B) = P(A and B)/P(B)

We want to find the probability that a student found a use for the class and found gainful employment after graduation, given that they took college statistics.

Let A be the event that a student found a use for the class and found gainful employment after graduation. 
Let B be the event that a student took college statistics.

We know:
P(A|B) = ?
P(A and B) = P(B) * P(A|B) = 0.28 * 0.93 = 0.2604
P(B) = 0.86

Now we can find P(A|B):
P(A|B) = P(A and B)/P(B) = 0.2604/0.86 = 0.3023

Therefore, the probability that a randomly selected student who took college statistics found a use for the class and found gainful employment after graduation is 0.3023 or approximately 0.2604. The closest option is A.

Twenty-Eight Percentof All People Who Take College Statistics Classes Claim