Question

A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. The survey also showed that 5% of the consumers were dissatisfied and had specifically complained about work by Plumber X. Plumber X does 40% of the plumbing jobs in the community.

1. What is the probability that a randomly selected consumer in this community will obtain an unsatisfactory plumbing job, given that Plumber X did the work?

2. What is the probability that a randomly selected consumer in this will obtain a  

satisfactory plumbing job, given that Plumber X did the work?

Answer 1

Let $A$ be the plumbing job done.

Let $U$ be the job is unsatisfactory.

So $P(A)=0.40$ and $P(U\cap A)=0.05.$

1.

$$P(U|A)=\dfrac{P(U\cap A)}{P(A)}=\dfrac{0.05}{0.40}=0.125$$

2.

$$P(U^C|A)=1-P(U|A)=1-0.125=0.875$$