Question

A survey of consumer showed that 10% were Dissatisfied with plumbing jobs done in their homes.
Half of the complaints dealt with plumber A, who does 40% of plumbing job in the town.

Find the probability that a consumer will obtain
a) Unsatisfactory plumbing job given the plumber was A
b) satisfactory plumbing job, given plumber was A

Answer 1

This is the solution manual please explain the number

Define the events: U: job is unsatisfactory A: plumber Adoes the job
a. P(U|A) = P(A∩U)/P(A) = P(A|U)P(U)/P(A) = .5*.1/.4 = 0.125
b.From part a. above, 1 – P(U|A) = 0.875.

Answer 2

The first part of the solution makes use of the following formula for conditional probability:
\[\large P(A | B)=\frac{P(A \cap B)}{P(B)}\ .............(1)\]
Using the formula in (1) for the question, we get:
\[\large P(U \cap A)=\frac{P(U \cap A)}{P(A)}=\frac{P(A \cap U)}{P(A)}\ .....(2)\]
Note: In equation (2) the interchange of U and A in the numerators of the fractions does not matter, the reason being that
\[\large P(U \cap A)=P(A \cap U)\]
@Let.Van Do you understand so far?