Finite probability help

Question

At a university, the probability that a first year student takes an Algebra class is 0.65, the probability the student takes a Biology class is 0.30, and the probability of taking neither is 0.25. Given the student is taking Algebra, what is the probability that he is taking Biology?

Answer 1

Draw a Venn diagram

P(A or B) = 1 .2= .75

P(A) = .65

P(B)=.3

P(A or B) = P(A) + P(B) - P(A and B)

.75 = .65 + .3 - P(A and B) => P(A and B) = .2

P(B|A) = P(A and B)/P(A) = .2/.65