Answer:
[tex] P(A) =0.85, P(B|A) =0.13[/tex]
And we want to find this probability: [tex] p(A \cap B)[/tex]. If we use the bayes rule we have this:
[tex] P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
And if we solve we got:
[tex] P(A \cap B) = P(B|A) P(A)[/tex]
And replacing we got:
[tex] P(B|A)= 0.13*0.85 = 0.1105[/tex]
Step-by-step 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:
[tex] P(A) =0.85, P(B|A) =0.13[/tex]
And we want to find this probability: [tex] p(A \cap B)[/tex]. If we use the bayes rule we have this:
[tex] P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
And if we solve we got:
[tex] P(A \cap B) = P(B|A) P(A)[/tex]
And replacing we got:
[tex] P(B|A)= 0.13*0.85 = 0.1105[/tex]
