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 events with P(A) = .4and P(B) = .7. a. ?If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. b.? ?What is the probability that at least one of the two projects will be successful? c. ?Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?

Answer : Step 1 of 3 : Given, 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 events with P(A) = .4 and P(B) = .7. a) A and B are independent. Happening of B does not depend on occurrence of A. thus not being successful an asian project does not affect probability of success in European project. Therefore, P(B ) = 1 - P(B) = 1 - 0.7 = 0.3 Step 2 of 3 : b) let the event be c c c P(C) = 1 - P(A B ) c c = 1 - P(A ) P(B ) = 1 - (1 - 0.4) (1-0.7) = 1 - (0.6) (0.3) = 0.82