A small town has two banks A and B It s estimated that 45 of

A small town has two banks A and B. It s estimated that 45% of the potential customers do business only with bank A, 30% only with bank B, and 15% with both banks A and B. The remaining 10% of the customers do business with none of the banks. If E1(E2) denotes the event of a randomly selected customer doing business with bank A(B), find the following probabilities: P(El), P(E2), P(EIflE2),P(E1E2) and P(E1 UE2)

Solution

First draw Venn diagram to have a clear picture

P(E1) = 0.60, P(E2) = 0.30, P(E1E2) = 0.15

P(E1\'E2\') = 1-0.15 = 0.85

P(E1\'UE2) = 1-0.60 = 0.40