Question

Problem 3-05 (Algorithmic) Brandon Lang is a creative entrepreneur who has developed a novelty soap item called Jackpot to target consumers with a gambling habit. Inside each bar of Jackpot shower soap is a single rolled-up bill of U.S. currency. The currency (rolled up and sealed in shrinkwrap) is appropriately inserted into the soap mixture prior to the cutting and stamping procedure. The distribution of paper currency (per 1000 bars of soap) is given in the following table.

Distribution of Paper Currency Prizes

Bill Denomination Number of Bills $

1   570  

5   210  

$10   140

$20   50

$50   27

$100   3  

Total   1000

If a customer buys 8 bars of soap, what is the probability that at least one of these bars contains a bill of $20 or larger? If required, round your answer to four decimal places.

Answer 1

Number of Bars are below 20$ = 920

Total number of bars = 1000

If customer buys 8 bars of soap, probabality that atleast one of these bars contains a bill of 20$ or larger

= 1 - P( zero bars contains a bill of 20$ or larger means all bar below 20$)

= 1 - [ 920C8 / 1000C8 ]

= 1 - [1.2346 x 10^19 / 2.4115 x 10^19]

= 1 - [ 0.5120]

= 0.4880