Answer all questions with explanation

A restaurant has decided to hang a decorative string light consisting of 50 bulbs. Suppose that in any given month, any one bulb fails with a probability of 0.1, independently of one another.

(b) How many bulbs are expected to fail in one month given there will be at least 5 failures?

(c) For a given bulb on the string, what is the probability it will last longer than 36 months?

(d) Suppose at the end of each month, the restaurant replaces all failed bulbs with new ones. What is the probability that all original 50 bulbs on the string will get replaced within the first 36 months of use?