Question

The proportion of individuals in a certain city earning more than ​$38 comma 00038,000 per year is 0.250.25. The proportion of individuals earning more than ​$38 comma 00038,000 and having a college degree is 0.120.12. Suppose that a person is randomly chosen and he turns out to be earning more than ​$38 comma 00038,000. What is the probability that he is a college​ graduate?

Answer 1

Answer: 0.48

Explanation:

Let , Event A =Individuals earning more than ​$38,000.

Event B =Individual have a college degree

Given : The proportion of individuals in a certain city earning more than ​$38,000 per year :P(A)= 0.25.

The proportion of individuals earning more than ​$38 comma 00038,000 and having a college degree is P(A and B)= 0.12.

Using conditional probability formula , we have

`P(B|A)=(P(A\ and\ B))/(P(B))\\\\`

i.e. Probability that an individual is a college​ graduate given that he is earning more than $38,000
`=(0.12)/(0.25)=0.48`

Hence, the required probability = 0.48