I have this problem:
A Ph.D. graduate has applied for a job with two universities: A and B. The graduate feels that she has a 60% chance of receiving an offer from university A and a 50% chance of receiving an offer from university B. If she receives an offer from university B, she believes that she has an 80% chance of receiving an offer from university A. a) What is the probability that both universities will make her an offer? b) What is the probability that at least one university will make her an offer? c) If she receives an offer from university B, what is the probability that she will not receive an offer from university A?
And I have done it like this:
A A' B 0.4 0.1 p(B)=0.5 B' 0.2 0.3 p(B')=0.5 p(A)=0.6 p(A')=0.4 p(A|B)=0.8 p(A and B)=p(B)p(A|B)=0.5(0.4)=0.4 a) p(both)=p(A and B)=0.4 b) p(at least 1)=1-p(none)= 1-p(A' and B')=0.7 c)p(A'|B)=p(B|A')p(A')/p(B)=(0.25(0.4))/0.5=0.2 p(B|A')=p(A' and B)/p(A')= 0.1/0.4=0.25
So is this the correct way of approaching it? Is it correct? Thanks.