Question: Assume that the bulbs in Problem are not replaced as they fail.
a. What fraction of the 6,000 bulbs are expected to fail in the first year?
b. What fraction of the bulbs surviving the first year are expected to fail in the second year?
c. What fraction of the bulbs surviving the nth year are expected to fail in year n = 1 for any value of n = 1, 2, . . . ?
d. Using the results of part (c), of the original 6,000 bulbs, how many would be expected to fail in the fourth year of operation?
Problem: Six thousand light bulbs light a large hotel and casino marquee. Each bulb fails completely at random, and each has an average lifetime of 3,280 hours. Assuming that the marquee stays lit continuously and bulbs that burn out are replaced immediately, how many replacements must be made each year on the average?