Two dice, win the sum only when the total is even

Question

You roll two fair six-sided dice. If the total is even you win that total in dollars. If the total is odd you win nothing. On average, how much do you win per roll?

Accepted Answer

Only the even totals pay, so I will find the chance and value of each even total. There are 6 	imes 6 = 36 equally likely rolls. The number of ways to make each even total: - Total 2: one way (1-1) - Total 4: three ways (1-3, 2-2, 3-1) - Total 6: five ways - Total 8: five ways - Total 10: three ways - Total 12: one way For each even total, multiply the total by how many ways make it, then add: 2(1) + 4(3) + 6(5) + 8(5) + 10(3) + 12(1) = 2 + 12 + 30 + 40 + 30 + 12 = 126. Odd totals contribute zero, so the whole payout across the 36 rolls is 126 dollars. Divide by 36: EV = \frac{126}{36} = \fr…

Two dice, win the sum only when the total is even

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