Question

All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is 0.70, the probability the second truck is available is 0.60, and the probability that both trucks are available is 0.49 What is the probability neither truck is available? (Round your answer to 2 decimal places.)

Answer 1

The probability that neither truck is available is 0.19

Explanation:

P(A) = Probability 1st truck available = 0.70

P(B) = Probability 2nd truck available = 0.60

P(A∩B) = Probability that both trucks are available = 0.49

P(A'∩B') = Probability that neither truck is avilable = ???

P(A∪B) = probability that 1st truck is available or 2nd truck is available or both trucks are available.

P(A∪B) = P(A) + P(B) - P(A∩B)

P(A∪B) = 0.70 + 0.60 - 0.49

P(A∪B) = 0.81 -----> this is the probability that any event happens

Let's find the probability that neither event happens P(A'∩B')

P(A'∩B') = 1 - P(A∪B)

P(A'∩B') = 1 - 0.81 = 0.19