Each person takes turns rolling two dice. If the sum is odd, the person playing odds gets points equal to the sum of the roll. If the sum is even, the person playing evens gets points equal to the sum of the roll. Note that the points earned is independent of who is rolling the dice. If Jessica is challenged to a game of Sums, which statement is accurate in every aspect in guiding her to the correct choice of choosing to play odds or evens?
Answer
A
cap e times evens will be more because there are more even numbers that result from rolling two dice. Therefore, Jessica should play evens.
B
cap e times evens will be more because the value of the even numbers on the dice are more. Therefore, Jessica should play evens.
C
cap e times evens is equal to cap e times odds because the different probabilities and values end up balancing out, creating a fair game. Therefore, Jessica may choose whichever she likes.
D
cap e times odds will be more because the probability for each odd number being rolled is greater. Therefore, Jessica should play odds.
Explanation
The expected points for odds are (3×2 + 5×4 + 7×6 + 9×4 + 11×2) ÷ 36 = 126 ÷ 36 = 3.5 per roll. For evens, they are (2×1 + 4×3 + 6×5 + 8×5 + 10×3 + 12×1) ÷ 36 = 126 ÷ 36 = 3.5 as well. The different probabilities and point values balance out, so the expected scores are equal and Jessica can choose either side.
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