A bank accepts rolls of pennies and gives 50 cents credit to a customer without counting the contents. Assume that a roll contains 49 pennies 30 percent of the time, 50 pennies 60 percent of the time, and 51 pennies 10 percent of the time.

(a) Find the expected value and the variance for the amount that the bank loses on a typical roll.
(b) Estimate the probability that the bank will lose at least 25 cents in 100 rolls.
(c) Estimate the probability that the bank will lose any money in 100 rolls.
(d) How many rolls does the bank need to collect to have a 99 percent chance of a net loss?