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) = 0.8 and P(B) = 0.4. Given that at least one of the two projects is successful, what is the probability that only the Asian project is successful?

Answer 1

54.55% probability that only the Asian project is successful

Explanation:

We use the conditional probability formula to solve this question. It is

`P(B|A) = (P(A \cap B))/(P(A))`

In which

P(B|A) is the probability of event B happening, given that A happened.

`P(A \cap B)` is the probability of both A and B happening.

P(A) is the probability of A happening.

In this question:

Event A: At least one of the projects is successful.

Event B: Only the Asian project is successful.

We use P(A) for event A and event B, not related to the P(A) and P(B) given in the exercise.

Probability that at least one of the projects is successful.

Either none are successful, or at least one is. The sum of the probabilities is 1.

The Asian project has a probability of 0.8 of being successfull, which means that it has a probability of 1 - 0.8 = 0.2 of not being successful.

Following the same logic, the event B has a probability of 1 - 0.4 = 0.6 of not being successful. So

`P(A) + 0.2*0.6 = 1`

`P(A) = 0.88`

Intersection:

Between at least one being successful and only the Asian project successfull is the Asian succesful(probability 0.8) and the European not successful(probability 1 - 0.4 = 0.6). So

`P(A \cap B) = 0.8*0.6 = 0.48`

What is the probability that only the Asian project is successful?

`P(B|A) = (0.48)/(0.88) = 0.5455`

54.55% probability that only the Asian project is successful