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) = 0.7 and P(B) = 0.4.

(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 not independent, then A' and B' are mutually exclusive.     Since the events are independent, then A' and B' are independent, too. Since the events are 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?

Answer 1

A : Event that the Asian project is successful.

B : Event that the European project is successful.

A and B are independent event.

We have given P(A) = 0.7 and P(B) = 0.4

a . In this part we have to find probability that the European project is not successful if the Asian project is not successful.

That is P(B'|A') = P(B' A') / P(A') = P(B') * P(A') / P(A') = P(B')

P(B') = 1 - P(B) = 1 - 0.4 = 0.6

b. In this part we have to find the probability that at least one of the two projects will be successful.

That is we have to find P(A B)

P(A B) = P(A) + P(B) - P(A B) = P(A) +P(B) - P(A)*P(B)

P(A B) = 0.7 + 0.4 - 0.7*0.4 = 0.82

c . Given that at least one of the two projects is successful, we have to find probability that only the Asian project is successful.

P(A B' | A   B) = (P([A B'] [A B]) / P(A   B)

= P([A B']) /P(A B)
=P(A)*P(B')/P(A B)
= (0.7)(0.6)/0.82

=0.5122