Use the following description to answer the next three (3) questions. An oil exp

Question

Use the following description to answer the next three (3) questions. 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)-0.40 and P(B)-0.70. * indepen aint If the Asian project is successful, what is the probability that the European project is also successful? A. 0.28 B. 0.40 C. 0.57 D. 0.70 E. 1.75 PCB)

Explanation / Answer

A = Asian project is successful.

B = European project is successful.

P(A) = 0.40, P(B) = 0.70

25) Since events A and B are independent. The occurence of event A has no effect on the occurence of event B. So the probability of the European project being successful is P(B) = 0.70. Option D.

26) Probability that atleast one of the two projects will be successful = P(AUB) = P(A) + P(B) - P(A B)

Since A and B are independent events. P(A B) = P(A).P(B)

So, P(AUB) = 0.40 + 0.70 - (0.40)*(0.70) = 1.10 - 0.28 = 0.82. Option C.

27) Probability that Asian project is successful and the European project is unsuccessful. In probability terms the even is represented as: P(A B`) , Since A and B are independent.

P(A B`) = P(A).P(B`) , P(B`) = 1 - P(B)

P(A B`) = 0.40 x (1-0.70) = 0.12. Option A.

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