Two dice are thrown at the same time. Determine the probability that the (i) sum of the numbers on the two dice is 5, and (ii) difference of the numbers on the two dice is 3.
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
Total possible outcomes when two dice are thrown = 6 × 6 = 36
(i) Sum of numbers on two dice = 5
Favourable outcomes: (1,4), (2,3), (3,2), (4,1) → 4 outcomes
$$P(\text{sum} = 5) = \frac{4}{36} = \frac{1}{9}$$
(ii) Difference of numbers on two dice = 3
Favourable outcomes: (4,1), (5,2), (6,3), (1,4), (2,5), (3,6) → 6 outcomes
$$P(\text{difference} = 3) = \frac{6}{36} = \frac{1}{6}$$
Source: Chapter 14, Example 13 / Exercise 14.1
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Explanation
- Always state total outcomes = 36 first (1 mark).
- For "difference = 3," consider both (a−b = 3) and (b−a = 3), giving 6 pairs — students often miss half of these.
- List favourable outcomes explicitly; examiners award a method mark for correct listing even if the final fraction has an error.
- Simplify the fraction to its lowest terms.