Two dice of different colours are thrown at the same time. Write down all the possible outcomes. What is the probability that :
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
When two dice are thrown, total number of possible outcomes = 6 × 6 = 36.
The possible outcomes are: (1,1), (1,2), ... (1,6), (2,1), (2,2), ... (2,6), (3,1) ... (6,6).
(i) Same number on both dice:
Favourable outcomes: (1,1), (2,2), (3,3), (4,4), (5,5), (6,6) → 6 outcomes
$$P(\text{same number}) = \frac{6}{36} = \frac{1}{6}$$
(ii) Different number on both dice:
$$P(\text{different number}) = 1 - P(\text{same number}) = 1 - \frac{1}{6} = \frac{5}{6}$$
Source: Chapter 14, Section 14.1
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Explanation
- Always state total outcomes (36 for two dice) first — examiners check this.
- For part (i), list all 6 favourable outcomes explicitly to show working.
- For part (ii), use the complement rule: P(E̅) = 1 − P(E). This saves time and shows conceptual understanding, earning full marks without listing all 30 outcomes separately.
- Parts (i) and (ii) carry about 1 mark each; the sample space listing carries 1 mark.