Andrea is a very good student. the probability that she studies and passes her mathematics test is 17/20. if the probability that andrea studies is 15/16, find the probability that andrea passes her mathematics test, given that she has studies.

Let B be the event that Andrea passes her test, and let A be the event 
that she studies. We are given that P(A and B) = 17/20, and that P(A) = 15/16. 

Now the probability that Andrea passes her test given that she has studied 
is represented by P(BlA). The formula your teacher gave you can be written as 
P(BlA) = P(A and B) / P(A). 

So P(BlA) = P(A and B) / P(A) = (17/20) / (15/16) = (17/20)*(16/15) = 68/75.