Suppose someone gives you 5 to 1 odds that you cannot roll two even numbers with

Question

Suppose someone gives you 5 to 1 odds that you cannot roll two even numbers with the roll of two fair dice. This means you win $5 if you succeed and you lose $1 if you fail. What is the expected value of this game to you? Should you expect to win or lose the expected value in the first game? What can you expect if you play 100 times? Explain. (The table will be helpful in finding the required probabilities.) Click the icon to view the table. What is the expected value of this game to you? Should you expect to win (or lose) an amount equal to the expected value in the first game? O Yes, you can expect to win (or lose) the expected value in the first game. O No, the outcome of one game cannot be predicted. What can you expect if you play 100 times? Explain this result Averaged over 100 games, you should expect to

Explanation / Answer

(a) P(getting even numbers on both die) = 9/36

expected value = (9/36)(5)+(-1)(27/36) = 0.5 dollars

(b) Yes you can expect to win the expected value in the fist game

(c) Expected value for 100 plays = 0.5*100 = 50 dollars

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