Suppose that you have 15 light bulbs in the house, and that the lifetime of each light bulb is independent of all the other bulbs. Assume that each light bulb's lifetime has an exponential distribution with parameter 1 (ie, the mean lifetime is 1 year).

a. What is the probability that exactly 8 of those 15 bulbs will burn out in the next 2 years?

b. Suppose instead that 14 of the bulbs have lifetimes that are exponentially distributed with parameter 1, and that the remaining bulb has a lifetime that is exponentially distributed with parameter 2 (its mean lifetime is year). What is now the probability that exactly 8 of the 15 bulbs fail before 2 years?