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- December 3rd 2013, 08:58 PM #1

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- December 3rd 2013, 08:59 PM #2

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## Analyzing Random Variables Expected Values

Would anyone be able to guide me in the right direction for this problem?

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.)

The expected payoff:

- December 3rd 2013, 09:22 PM #3

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## Re: Analyzing Random Variables Expected Values

This is simply Pr[rolling a 7]*10 - Pr[rolling 11]*20

Any particular dice roll has Pr=1/36, assuming 6 sided dice

you can roll a 7 via 1,6 2,5 3,4 4,3 5,2 6,1 so the overall Pr[7] = 6/36 = 1/6

you can roll an 11 via 5,6 6,5 so the overall Pr[11] = 2/36 = 1/18

E = 1/6*10 - 1/18*20 = 10/6 - 20/18 = 10/18 = 5/9 ~ 56 cents