Question

In a bookstore thirty five percent of customers who are not teachers order pencils. Fifty percent of all customers are teachers. Of the customers who are teachers, twenty five percent order pencils. If a randomly chosen customer orders pencils, what is the probability that customer is a teacher?

Answer 1

In a bookstore, 35% of customers who are not teachers, order pencils.

50% of all customers are teachers.

Of the customers who are teachers, 25% order pencils.

Now, we denote the events

T=Event that a customer is tecaher

P=Event that a customer orders pencils

It is given that

Now, we have to find the probability that a customer is a teacher, given that the chosen customer orders pencils.

So, basically we have to find

Now, first we have to find the probability that a chosen customer orders pencils.

So,

By total probability theorem, this becomes,

Now,

By Bayes theorem, this becomes

The answer is

If a chosen customer orders pencils, the probability that he is a teacher, is 0.4167.