Question

Two dice are rolled. Find the probability of getting

A. A sum of 5,6,7

B. Doubles or sum of 6 or 8

C. A sum greater than 8 or less than 3

D Based on the answers to parts a, b, c which is least likely to occur? explain why?

Step 1

**Sample space for rolling two dice:**

It is given that two dice are rolled. The number of possible outcomes for rolling two dice is 36. The sample space is as follows.

Step 2

**A. Probability of getting a sum of 5,6,7:**

The probability of getting a sum of 5,6,7 is *P*_{5} + *P*_{6 }+ *P*_{7}

The possible outcomes for which the pair sum is 5 in the total of 36 outcomes are (1, 4), (2, 3), (3, 2), (4, 1). Thus, there are 4 favorable outcomes for which the pair sum is 5.

The possible outcomes for which the pair sum is 6 in the total of 36 outcomes are (1, 5), (2, 4), (3, 3), (4, 2), (5, 1). Thus, there are 5 favorable outcomes for which the pair sum is 6.

The possible outcomes for which the pair sum is 7 in the total of 36 outcomes are (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1). Thus, there are 6 favorable outcomes for which the pair sum is 7.

The probability of getting a sum of 5,6,7 is **0.4167** from the calculations given below.

Step 3

**B. Probability of getting doubles or sum of 6 or 8 Probability of getting doubles or sum of 6 or 8:**

The possible outcomes of getting doubles are (1, 1), (2, 2), (3, 3), (4, 4), (5, 5), and (6, 6). Thus, there are 6 favorable outcomes.

The possible outcomes of getting a sum of 6 or 8 are (1, 5), (2, 4), (2, 6), (3, 3), (3, 5), (4, 2...

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