# Question

In the casino game called high–low, there are three possible bets. Assume that $1 is the size of the bet. A pair of fair six-sided dice is rolled and their sum is calculated. If you bet low, you win $1 if the sum of the dice is {2, 3, 4, 5, 6}. If you bet high, you win $1 if the sum of the dice is {8, 9, 10, 11, 12}. If you bet on {7}, you win $4 if a sum of 7 is rolled. Otherwise, you lose on each of the three bets. In all three cases, your original dollar is returned if you win. Find the expected value of the game to the bettor for each of these three bets.

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