Refer to the Jackpot soap scenario in Problem 24. After the sale of the original 1,000 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 24. A customer is interested in analyzing the number of bars that they need to buy so that the last bar purchased is the third bar to contain a bill of at least $20 value. This required number of bars is uncertain.

a. What type of random variable describes the number of bars containing a bill of less than $20 value that are purchased before obtaining the third bar to contain a bill of at least $20 value?

b. Construct a model to simulate the number of bars that need to be purchased so that the last bar purchased is the third bar to contain a bill of at least $20 value.

c. On average, how many bars of soap will a customer need to buy before obtaining three bars of soap containing a bill of at least $20 value?

d. What is the probability that the customer will need to buy more 50 bars of soap?

Problem 24

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 1,000 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 1,000 bars is given in the following table:

If a customer buys 40 bars of soap, the number of bars that contain a $50 or $100 bill is uncertain.

Transcribed Image Text:

Bill Denomination ($) 1 5 10 20 50 100 Total Number of Bills 520 260 130 60 29 1 1,000