# Due Date: Friday, October 2, 10:30 am

This is an INDIVIDUAL Project!

I) Scratching!

Chances of Winning the Harley- Davidson Scratch Game

Prize

Chances

\$2

1 in 10

\$3

1 in 13.79

\$5

1 in 30.77

\$10

1 in 40

\$12

1 in 100

\$20

1 in 200

\$50

1 in 727.27

\$100

1 in 7,500

\$500

1 in 59,294.12

Motorcycle (\$15,000)

1 in 560,000

\$25,000

1 in 1,028,160

## OVERALL

1 in 4.06

1. Using the table at the right, determine the expected value for this Harley-Davidson scratch game.   Note that the cost of a single ticket is \$2.
2. Using the table of actual plays below, compare the theoretical expected value to the average winnings per play for the class’ 270 plays.  Did what you expected to happen actually happen?  Explain.

## Scratch Lottery Results

There were a total of 270 "scratches".  The table below lists the students' winning results.

 Winnings -> 2 3 5 10 12 20 50 100 500 15000 25000 Name Student 1 1 0 0 1 0 0 0 1 2 0 0 Student 2 1 1 1 0 0 0 0 1 0 1 0 Student 3 0 0 0 0 0 0 0 1 0 0 0 Student 4 3 1 0 0 0 0 3 0 0 1 0 Student 5 1 1 0 0 0 0 0 0 0 1 0 Student 6 0 2 0 2 0 1 0 0 0 0 2 Student 7 0 1 0 1 0 1 2 1 1 0 0 Student 8 3 0 0 0 0 0 0 0 0 1 0 Student 9 3 0 1 1 0 0 1 0 0 0 3

1. Compare the theoretical overall chances of winning to the class’ 270 plays.

II) Probability

A lot of 50 items from a manufacturing process is know to contain 20 defective items and 30 nondefective.  If a sample of 10 items is selected at random, what is the probability that:

a) the sample has 6 defective and 4 nondefective items?

b) the sample has no defective items?

c) the sample has at least one defective item?