8. An oil exploration company currently has two active projects, one in Asia and

Question

8. 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) = 0.8 and P(B) =0.6. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? (5 pts) (b) What is the probability that at least one of the two projects will be successful? (5 pts)

Explanation / Answer

a) Since A and B are independent,

P(BC | Ac) = P(BC)

And hence,

P(BC | Ac) = 1 - P(B) = 1 - 0.6 = 0.4

b) P(At least one out of two projects gets successful)

= 1 - P(No project gets successful)

= 1 - (1 - P(A))(1 - P(B))

= 1 - (1 - 0.8)(1 - 0.6)

= 0.92

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