All Seasons Plumbing has two service trucks that frequently

All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is .71, the probability the second truck is available is .56, and the probability that both trucks are available is .40:

What is the probability neither truck is available?

Solution

Let

A = first truck is available
B = second truck is available

Thus,

P(neither is available) = P(A U B)\'

As

P(A U B) = P(A) + P(B) - P(A and B) = 0.71+0.56-0.40 = 0.87

Then

P(A U B)\' = 1 - P(A U B) = 1 - 0.87 = 0.13 [ANSWER]