# Math

A carnival game consists of rolling a single fair die, with the following results: you win \$8 for a 6, \$7 for a 5, and lose \$3 for any other number. Set a probability distribution, and calculate (already did) the

Expected value = .50
Variance= 24.58
standard deviation= 4.96

What fee should be charged to make it a fair game?

1. 👍 0
2. 👎 0
3. 👁 90
1. The equally probable monetary results of a toss are +8,+7,-3, -3, -3 and -3. The expected result is (15-12)/6 = 0.50, a 50 cent gain. I assume you calculated the variance correctly also.

The breakeven charge for a toss should be 50 cents. This is true regardless of the standard deviation. If the House charges more than 50 cents, the player will lose in the long run. Sixty cents would be a fair charge that allows a House profit. As a sucker bet, they might try to charge \$1.

1. 👍 0
2. 👎 0
posted by drwls
2. If all the possible outcomes are independent, one merely has to add the expected return of each outcome, so...

"fair game" charge = 8(1/6) + 7(1/6) + (-3)(4/6)
= .50

So in the "long run" at a 50 cents charge both the player and the house would break even.

1. 👍 0
2. 👎 0
posted by Reiny

## Similar Questions

1. ### Math

A game consists of you rolling one fair 6-sided die and observing the number that appears uppermost. If you roll a 2 or a 4, then you win \$10. If you roll a 6, then you win \$20. If you roll any other number, then you do not win

asked by Anonymous on November 29, 2017
2. ### Statistics

A gambling game works as follows: you flip a fair coin and roll a fair six-sided die. You will be paid \$2 if you roll a 6 and \$1 if you get a head and an odd number of spots. Otherwise, you have to pay \$2.50. a) What is the

asked by alle on November 4, 2017
3. ### Math

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by Anonymous on November 14, 2009
4. ### Math

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be consdiered a fair game?

asked by Michelle on December 12, 2009
5. ### MATH Prob.

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by Twg on August 11, 2009
6. ### math

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by Anonymous on March 5, 2010
7. ### Math

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by Lisa on May 18, 2010
8. ### Math-Fair Game question

the game of dots is played by rolling a fair die and receiving 1\$ for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by C.J on January 23, 2010
9. ### Math

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by Nicole on December 2, 2009
10. ### math fair

The game of dots is played by rolling a fair die and receiving \$1 for each dot showing on the top face of the die. What cost should be set for each roll if the game is to be considered a fair game?

asked by jason on October 21, 2009

More Similar Questions