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.

• Find the expected value and the variance for the amount that the bank loses on a typical roll.
• Estimate the probability that the bank will lose more than 25 cents in 100 rolls.
• Estimate the probability that the bank will lose exactly 25 cents in 100 rolls.
• Estimate the probability that the bank will lose any money in 100 rolls.
• How many rolls does the bank need to collect to have a 99 percent chance of a net loss?