Question

All Seasons Plumbing has two service trucks that frequently need repair. If the probability the first truck is available is 0.75, the probability the second truck is available is 0.50, and the probability that both trucks are available is 0.30. What is the probability neither truck is available

Answer 1

Answer: There is a probability of 0.05 that there is neither truck is available.

Step-by-step explanation:

Since we have given that

Probability that the first truck is available = 0.75

Probability that the second truck is available = 0.50

Probability that both trucks are available = 0.30

So, probability that either first truck or second truck is available is given by

$P(A\cup B)=P(A)+P(B)-P(A\cap B)\\\\P(A\cup B)=0.75+0.50-0.30\\\\P(A\cup B)=0.95$

We need to find the probability that neither truck is available.

so, P(A∪B)'=1-P(A∪B)

$P(A\cup B)'=1-0.95=0.05$

Hence, there is a probability of 0.05 that there is neither truck is available.