Two factories supply light bulbs to the market. Bulbs from factory X work for over 5000 hours in 99% of cases, whereas bulbs from factory Y work for over 5000 hours in 95% of cases. It is known that factory X supplies 60% of the total bulbs available in the market. (a) What is the probability that a purchased bulb will work for longer than 5000 hours? (b) Given that a light bulb works for more than 5000 hours, what is the probability that it was supplied by factory Y ? (c) Given that a light bulb work does not work for more than 5000 hours, what is the probability that it was supplied by factory X?