Question

Two dice are rolled. Find the probability of getting a. A sum of 5, 6, or 7 b. Doubles or a sum of 6 or 8 c. A sum greater than 8 or less than 3 d. Based on the answers to parts a, b, and c, which is least likely to occur

Answer 1

The answer is below

Explanation:

The possible outcome from rolling two dice is:

1,1 1,2 1,3 1,4 1,5 1,6

2,1 2,2 2,3 2,4 2,5 2,6

3,1 3,2 3,3 3,4 3,5 3,6

4,1 4,2 4,3 4,4 4,5 4,6

5,1 5,2 5,3 5,4 5,5 5,6

6,1 6,2 6,3 6,4 6,5 6,6

The total number of outcomes = 36

a)

P(sum of 5) = 4/36, P(sum of 6) = 5/36, P(sum of 7) = 6/36

Hence:

P(sum of 5 or sum of 6, or sum of 7) = P(sum of 5) + P(sum of 6) + P(sum of 7) = 4/36 + 5/36 + 6/36

P(sum of 5, 6, or 7) = 15 / 36

b)

P(doubles) = 6/36, P(sum of 6) = 5/36, P(sum of 8) = 5/36

Hence:

P(doubles or sum of 6 or sum of 8) = P(doubles) + P(sum of 6) + P(sum of 8) = 6/36 + 5/36 + 5/36

P(doubles or sum of 6 or sum of 8) = 16 / 36

c)

P(sum greater than 8) = 10/36, P(sum lesser than 3) = 1/36

P(sum greater than 8 or less than 3) = P(sum greater than 8) + P(sum lesser than 3) = 10/36 + 1/36

P(sum greater than 8 or less than 3) = 11 / 36

Part c has the least probability of occurrence, hence c is least likely to occur.