6 An oil exploration company currently has two active projec

(6) An oil exploration company currently has two active projects, one in Asia and the other in Europe. Let A be the event that the Asian project is successful and B be the event that the European project is successful. Suppose that A and B are independent event with P(A) = .4 and P(B) = .7. (a) If the Asian project is not successful, what is the probability that he European project is also not successful? Explain your reasoning. (b) What is the probability that at least one of the two projects will he successful? (e) Given that at least one of the projects is successful, what is the probability that only the Asian project is successful?

Solution

Since the events are independent, then A\' and B\' are independent, too.

P(A U B)=P(A)+P(B)-P(A)P(B) =0.2+0.5-0.2*0.5=0.6

P(B\')=1-P(B)=1-0.5=0.5

P(AB\'|A U B)=P(AB\')/P(AUB) =0.5*0.5/0.6=0.4167