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A survey of consumers in a particular community showed
Chapter 2, Problem 76E(choose chapter or problem)
Problem 76E
A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. Half the complaints dealt with plumber A, who does 40% of the plumbing jobs in the town. Find the probability that a consumer will obtain
a an unsatisfactory plumbing job, given that the plumber was A.
b a satisfactory plumbing job, given that the plumber was A.
Questions & Answers
QUESTION:
Problem 76E
A survey of consumers in a particular community showed that 10% were dissatisfied with plumbing jobs done in their homes. Half the complaints dealt with plumber A, who does 40% of the plumbing jobs in the town. Find the probability that a consumer will obtain
a an unsatisfactory plumbing job, given that the plumber was A.
b a satisfactory plumbing job, given that the plumber was A.
ANSWER:
Solution :
Step 1 of 2:
Let A be the plumbing job done.
Let U be the job is unsatisfactory.
We know that the plumbing jobs in the town is 40% and the jobs done in their homes is 50%.
So P(A)=0.40 and P(U)=0.10.
Our goal is:
a). We need to find an unsatisfactory plumbing job.
b). We need to find a satisfactory plumbing job.
a).
Now we have to calculate an unsatisfactory plumbing job.
Given that the plumber in A.
Now we use the bayes theorem to calculate.
The formula of P(U/A) is
Here
.
Then,
0.125
Therefore, an unsatisfactory plumbing job is 0.125.