Question

A manufacturer obtains​ clock-radios from three different​ subcontractors, 40% from Upper B1, 20% from Upper B2 and 40​% from Upper B3. The defective rates for​ clock-radios from these subcontractors are 3​%, 2 % and 5​% respectively. If a defective​ clock-radio is returned by a​ customer, what is the probability that a defective​ clock-radio came from subcontractor Upper B1​?

Answer 1

A manufacturer obtains clock radios from 3 different subcontractors, 40% from Upper B1, 20% from Upper B2, and 40% from Upper B3.

So, the probability that a randomly selected clock radio came from Upper B1, is 0.4.

The probability that a randomly selected clock radio came from Upper B2, is 0.2.

The probability that a randomly selected clock radio came from Upper B3, is 0.4.

ie. we can write this as

The defect rates for clock radios from these subcontractors are 3%, 2% and 5%.

So,

Now, we have to find the probability that a clock radio came from Upper B1, given that it was defective.

ie. to find

First, we find the probability that a randomly selected clock radio is defective.

=

Now, by total probability theorem, we can write this as

=

=

=

=

What we actually have to find

=

=

=

=

=

So, if a defective clock radio is returned by a customer, the probability that a defective clock radio came from subcontractor Upper B1, is 1/3.