Solved – check if I’m correct, with conditional and bayes

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.

So the answer is yes this is correct, there is another way to get b) without the 1-p formula like p(A or B)= p(A)+ p(B) – p(A and B), but I wanted to see the conditionals and use it. Thanks.

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