Question

An ordinary (fair) die is a cube with the numbers 1 through 6 on the sides (represented by painted spots). Imagine that such a die is rolled twice in succession and that the face values of the two rolls are added together. This sum is recorded as the outcome of a single trial of a random experiment. Compute the probability of each of the following events:

Event A: The sum is greater than 8.

Event B: The sum is an odd number.

Write your answers as exact fractions.

P (A)=

P (B)=

Answer 1

Probability = Favourable outcomes / Total Outcomes

Total outcomes: When 1 dice is rolled 2 times, the Total outcomes = 6² = 36

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Favourable outcomes for event A: Sum is greater than 8.

Sum of 9: (3,6) (6,3) (4,5) (5,4) = 4 outcomes

Sum of 10: (4,6) (6,4) (5,5) = 3 outcomes

Sum of 11: (5,6) (6,5) = 2 outcomes

Sum of 12: (6,6) = 1 outcome

Total Favourable Outcomes = 4 + 3 + 2 + 1 = 10

Therefore P(A) = 10/36 = 5/18

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Total Favourable outcomes for B: The sum is odd (Sum is 3,5,7,9,11)

Sum of 3: (1, 2) (2, 1) = 2 outcomes

Sum of 5: (1,4) (4,1) (2,3) (3,2) = 4 outcomes

Sum of 7: (1,6) (6,1) (2,5) (5,2) (3,4) (4,3) = 6 outcomes

Sum of 9: (3,6) (6,3) (4,5) (5,4) = 4 outcomes

Sum of 11: (5,6) (6,5) = 2 outcomes

Total Favourable outcomes for B = 2 + 4 + 6 + 4 + 2 = 18

Therefore P(B) = 18/36 = 1/2

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