Suppose that two factories supply light bulbs to the market. Factory X’s bulbs work forever in 99% of cases, whereas factory Y’s bulbs work forever in 95% of cases. It is known that factory X supplies 60% of the total bulbs available and Y supplies 40% of the total bulbs available.
a) What is the chance that a purchased bulb will work forever?
b) Given that a purchased bulb will work forever, what is the chance that it was made in Factory X?