Question

Find the probability that the sum is as stated when a pair of dice is rolled. (Enter your answers as fractions.) (a) 8 or 11 (b) 8 or 11 or doubles

Answer 1

Probability = Favorable outcomes / Total Outcomes

When a pair of dice is rolled, the total outcomes = 6² = 36 (for n dice it is 6ⁿ)

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(a) P(Sum is an 8 or a 11)

Favorable outcomes:

Sum of 8 = (2 6) (6 2) (3 5) (5 3) (4 4) = 5 cases

Sum of 11 = (5 6) (6 5) = 2 cases

Total Favorable outcomes = 5 + 2 = 7

Therefore the required probability = 7/36 = 0.1944

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(b) P(sum of 8 or 11 or doubles)

Favorable outcomes for 8 or 11 = 7 (as calculated in a)

Favorable outcomes for doubles = (1 1) (2 2) (3 3) (4 4) (5 5) (6 6) = 6

Total Favorable outcomes = 7 + 6 = 13

Therefore the required probability = 13/36 = 0.3611

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