Question

In a throw of a pair of dice, find the probability of getting a sum more than 7.

Answer 1

Given: A pair of fair dice is thrown; find the probability that the sum is more than 7.

Step-wise calculation:

1. Total possible outcomes

= 6 × 6

= 36

2. Sums greater than 7 are 8, 9, 10, 11, 12.

Count favourable outcomes:

Sum = 8: 5 outcomes (2 + 6, 3 + 5, 4 + 4, 5 + 3, 6 + 2)

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

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

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

Sum = 12: 1 outcome (6 + 6)

Total favourable

= 5 + 4 + 3 + 2 + 1

= 15

3. Probability = `"Favourable"/"Total"`

= `15/36`

Divide numerator and denominator by 3 = `5/12`.

The probability of getting a sum more than 7 is `5/12`.