An oil exploration company currently has two active proj- ects, 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 and . a. If the Asian project is not successful, what is the proba- bility that the European project is also not successful? Explain your reasoning. b. What is the probability that at least one of the two proj- ects 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? P(A) 5 .4 P(B) 5 .7

a) P(B'|A') = P(B') = 1 - 0.7 = 0.3.

The reasoning is that: since, events A and B are independent, then, events A' and B' are also independent and for independent events, P(A|B) = P(A).

b) P(A u B) = 0.82

c) P[(A n B')|(A u B)] = 0.146

Step-by-step explanation:

P(A) = 0.4

P(B) = 0.7

A and B are independent events.

P(A') = 1 - 0.4 = 0.6

P(B') = 1 - 0.7 = 0.3

a) If the Asian project is not successful, what is the proba- bility that the European project is also not successful?

P(B'|A') = P(B') = 1 - 0.7 = 0.3

The reasoning is that: since, events A and B are independent, then, events A' and B' are also independent and for independent events, P(A|B) = P(A).

b) The probability that at least one of the two projects will be successful = P(A u B)

P(A u B) = P(A) + P(B) - P(A n B) = 0.4 + 0.7 - (0.4)(0.7) = 0.82

OR

P(A u B) = P(A n B') + P(A' n B) + P(A n B) = (0.4)(0.3) + (0.6)(0.7) + (0.4)(0.7) = 0.82

c) Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?

P[(A n B')|(A u B)] = }P(A n B') n P(A u B)]/P(A u B) = P(A n B')/P(A u B) = (0.4)(0.3)/(0.82)

P[(A n B')|(A u B)] = 0.146

Hope this Helps!!!

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step-by-step explanation: