Qusetion: Refer to the jackpot soap scenario in Problem. After the sale of the original 1000 bars of soap, jackpot soap went viral, and the soap has become wildly popular. Production of the soap has been ramped up so that now millions of bars have been produced. However, the distribution of the bills in the soap obeys the same distribution as outlined in Problem 23. On average, how many bars of soap will a customer have to buy before purchasing three bars of soap each containing a bill of at least $20 value? Use the negative binomial distribution in ASP to answer this question.
Problem: A creative entrepreneur has created a novelty soap called jackpot. Inside each bar of jackpot soap is a rolled-up bill of U.S. currency. There are 1000 bars of soap in the initial offering of the soap. Although the denomination of the bill inside a bar of soap is unknown, the distribution of bills in these first 1000 bars is given in the following table:
Bill Denomination Number of Bills
$1 520
$5 260
$10 130
$20 60
$50 29
$100 1
Total 1000
How many bars of soap does a customer have to buy so that, on average, she has purchased two containing a $50 or $100 bill?