Question

The probability that a student will take loans to pay for their undergraduate education is 0.85, and the probability that a student will go to graduate school given that the student took loans to pay for their undergraduate education is 0.13. What is the probability that a student will go to graduate school and take loans to pay for their undergraduate education

Answer 1

`P(A) =0.85, P(B|A) =0.13`

And we want to find this probability:
`p(A \cap B)`. If we use the bayes rule we have this:

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

And if we solve we got:

`P(A \cap B) = P(B|A) P(A)`

And replacing we got:

`P(B|A)= 0.13*0.85 = 0.1105`

Explanation:

For this case we define the following notation:

A= A student will take loans to pay for their undergraduate education

B|A= A student will go to graduate school given that the student took loans to pay for their undergraduate education

And we have the following probabilities:

`P(A) =0.85, P(B|A) =0.13`

And we want to find this probability:
`p(A \cap B)`. If we use the bayes rule we have this:

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

And if we solve we got:

`P(A \cap B) = P(B|A) P(A)`

And replacing we got:

`P(B|A)= 0.13*0.85 = 0.1105`