Two number cubes are rolled .both cubes are

Labelled to 6. The numers rolled are added . What is the probability of each outcome? A) the sum is 12. B) the sum is less then 4. C) the sum is 7. D) the sum is 2.

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To find the probability of each outcome, we need to determine the total number of possible outcomes and the number of favorable outcomes for each case.

In this scenario, two number cubes are rolled. Since each cube has six sides labeled from 1 to 6, the total number of possible outcomes is found by multiplying the number of sides on each cube: 6 * 6 = 36.

A) To find the probability of getting a sum of 12, we need to determine the number of favorable outcomes (when both dice show 6). There is only one favorable outcome, as only one combination of two dice will give a sum of 12. Therefore, the probability of getting a sum of 12 is 1/36.

B) To find the probability of getting a sum less than 4, we determine the number of favorable outcomes. These include the combinations (1, 1), (1, 2), (2, 1), and (2, 2). There are four favorable outcomes. Hence, the probability of getting a sum less than 4 is 4/36, which can be simplified to 1/9.

C) To find the probability of getting a sum of 7, we need to determine the number of favorable outcomes. These include the combinations (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), and (6, 1). There are six favorable outcomes. Consequently, the probability of getting a sum of 7 is 6/36, which simplifies to 1/6.

D) To find the probability of getting a sum of 2, we determine the number of favorable outcomes. In this case, there is only one favorable outcome, namely (1, 1). Thus, the probability of getting a sum of 2 is 1/36.

In summary:
A) Probability of sum 12: 1/36
B) Probability of sum less than 4: 1/9
C) Probability of sum 7: 1/6
D) Probability of sum 2: 1/36