# Fair dice roll. The expected payoff?

• Dec 3rd 2013, 09:02 PM
Andi963258741
Fair dice roll. The expected payoff?
Consider the following game: Two fair dice are rolled. If the sum is 7, you win \$ 10. If the sum is 11, you lost \$ 20. What is the expected payoff for this game? (Round to the nearest penny.)
What is the expected payoff:
• Dec 3rd 2013, 09:11 PM
LimpSpider
Re: Fair dice roll. The expected payoff?
If the sum is neither 7 or 11? What then?
• Dec 3rd 2013, 09:17 PM
Andi963258741
Re: Fair dice roll. The expected payoff?
Not sure because this is all the information the book provided. I'm guessing zero.
• Dec 3rd 2013, 09:28 PM
Andi963258741
Re: Fair dice roll. The expected payoff?
I figured it out the expected value is \$0.55.
• Dec 4th 2013, 11:33 AM
HallsofIvy
Re: Fair dice roll. The expected payoff?
Assuming that there is neither loss nor gain if the roll is anything other than 7 or 11, it's a straightforward calculation. The probability of rolling "7" is 1/6 while the probability of rolling "11" 1/18. The expected value is 10(1/6)- 20(1/18)= 30/18- 20/18= 10/18= 5/9 dollars which is \$0.55 approximately.