A company is buying certain machine pieces from three differ

A company is buying certain machine pieces from three different vendors.

Vendor A’s machine you get are broken 15% of times vendor B’s 20% and vendor C 30% of time. Overall the company receives broken machines 20% of time. An inspector randomly chooses one of the machines. What is a probability that the machine is broken and from vendor A?

Solution

The probability of choosing a broken machine is 0.20.

The probability that the broken machine belongs to vendor B is 0.20.

Thus, the probability that the machine is broken and from vendor A is 0.20*0.20=0.04