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

Question

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) = 0.9 and P(B) = 0.3. (a) If the Asian project is not successful, what is the probability that the European project is also not successful? Explain your reasoning. Since the events are independent, then A' and B' are not independent. Since the events are independent, then A' and B' are independent. Since the events are independent, then A' and B' are mutually exclusive. Since the events are not independent, then A' and B' are mutually exclusive. (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?

Explanation / Answer

a)

probabilty that european project is not successful given Asian project not succesful=P(B')=1-P(B)=1-0.3=0.7

since the events are independent, then A' and B' are independent.

b)

probabilty that at least one of the project is succesful=P(AUB)=P(A)+P(B)-P(A)*P(B)=0.9+0.3-0.9*0.3=0.93

c)

probabilty that only Asian project succeful given at least one project is succesful =P(AnB'|AUB)=(0.9*0.7)/0.93

=0.677

please revert

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