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:

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.