Multiple choice

Michael has two dice, each with faces labeled with the numbers -12, -8, -4, 4, 8, and 12. He rolls the two dice and adds the resulting numbers. Quantity A Probability that the sum is greater than zero Quantity B Probability that the sum is less than zero

  1. Quantity A is greater.

  2. Quantity B is greater.

  3. The two quantities are equal.

  4. The relationship cannot be determined from the information given.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The set of values is {-12, -8, -4, 4, 8, 12}. Since the distribution is symmetric around zero, the probability of getting a positive sum is equal to the probability of getting a negative sum. The only case where the sum is zero is when the two dice show additive inverses (e.g., -12 and 12, or 4 and -4).

AI explanation

Because each positive number on a die has a corresponding negative number (such as 12 and -12), every possible sum greater than zero has a matching sum less than zero. For example, rolling a 12 and an 8 gives a sum of 20, but rolling a -12 and a -8 gives a sum of -20. Therefore, the number of outcomes resulting in a positive sum exactly equals the number of outcomes resulting in a negative sum, making the two probabilities equal.

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