statistics

Project Description:

the governor of alabama promised that, if elected, he would develop an “education lottery” that would allow all students in alabama with good grades to go to college free. he has proposed the following game:

1. the game would be played weekly with drawings made every saturday night,
2. contestants would pay $1 for each chance to play the game,
3. contestants would select 6 different numbers from 1 to 49,
4. 49 balls, numbered 1 to 49, would be placed in a barrel,
5. 6 balls would be randomly drawn from the barrel without replacement,
6. contestants win a predetermined amount a cash if they match 1, 2, 3, 4, 5, or all 6 numbers,
7. the payoff for each possible number of matching numbers is provided in the table below.

matching numbers prize
1 $1
2 $10
3 $100
4 $1,000
5 $10,000
6 $100,000
note the following:

• the $1 fee to play the game is a sunk cost for the contestant. that is, regardless of how many, if any, numbers the contestant matches, the contestant does not get the $1 back. in the case of the contestant matching 2 numbers, the contestant pays $1 to play and wins $10 so the contestant’s net winnings are $9.

• the grand prize is fixed at $100,000, unlike other lotteries where the amount varies each week according to the number of contestants and winners during the previous week.

the governor comes to you, a master statistician, and asks you to calculate the probability of winning each prize. you oblige the governor with the following accurate probabilities.

matching numbers prize probability
1 $1 0.4130195
2 $10 0.1323780
3 $100 0.0176504
4 $1,000 0.0009686
5 $10,000 0.0000184
6 $100,000 0.0000001

louie, your get-rich-quick cousin, tells you he’s going to play the game each week for the next 52 weeks and at the end of the year he expects to have “ pocketed” almost $200. is he correct? does the governor need to re-think his lottery game? do you have any suggestions for him?
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Price Type: Negotiable

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