Question

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

Answer 1

Given: A pair of fair six-sided dice is thrown once; find P(sum < 7).

Step-wise calculation:

1. Total possible outcomes

= 6 × 6

= 36

2. Sums less than 7 are 2, 3, 4, 5, 6.

Count outcomes for each:

Sum = 2: (1, 1) → 1 outcome

Sum = 3: (1, 2), (2, 1) → 2 outcomes

Sum = 4: (1, 3), (2, 2), (3, 1) → 3 outcomes

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

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

3. Number of favourable outcomes

= 1 + 2 + 3 + 4 + 5

= 15

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

= `15/36`

= `5/12`

The probability of getting a sum less than 7 is `5/12` (≈ 0.4167).