Please help!!!

Question

The probability that sue will live on campus and buy a new car is 0.34. If the probability that she will live on campus is 0.53, find the probability that she will buy a new car, given that she lives on campus.

Answer 1

Let A be the event that Sue will buy a new car.

Let B be the event that Sue lives in campus.

We are trying to solve for P(A|B), the conditional probability that Sue will buy a new car, given that she lives on campus.

 

This is computed as
P(A|B) = P(AB)/P(B).

 

Now, we can substitute in known values.

P(AB) is the probability that Sue will buy a new car AND live on campus.  This is 0.34.

P(B) is the probability that Sue lives on campus.  This is 0.53.

 

P(A|B) = P(AB)/P(B)

          = 0.34/0.53.