Question

A company decides to check on the accuracy of invoicing. Invoices are prepared by Alicia, Linda

and Jane. A sample of 500 invoices are selected. Two hundred were prepared by Alicia, 120

by Linda and 180 by Jane. The error rates by Alicia, Linda and jane were found to be 25, 3%

and 4% respectively. From the sample of 500 invoices, one invoice was selected.

a) Draw a tree diagram for the above information

b) What is the probability that the invoice contains an error?

c) What is the probability that the invoice was prepared by Alicia, given that it contains no

error?

Answer 1

a)

b)

The Law of Total Probability

$$P(E)=P(E|A)P(A)+P(E|L)P(L)+P(E|J)P(J)$$

$$=0.10+0.0072+0.014=0.1212$$

c) Bayes’ Theorem

$$P(A|\bar{E})=\dfrac{P(\bar{E}|A)P(A)}{P(\bar{E}|A)P(A)+P(\bar{E}|L)P(L)+P(\bar{E}|J)P(J)}$$

$$=\dfrac{0.30}{0.30+0.2328+0.3456}=0.34130$$