Two dice are thrown at the same time. Determine the probability that the difference of the numbers on the two dice is 2.
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
Total possible outcomes when two dice are thrown = 6 × 6 = 36
Favourable outcomes (difference = 2, i.e., |die1 − die2| = 2):
(1,3), (2,4), (3,5), (4,6) → difference 2
(3,1), (4,2), (5,3), (6,4) → difference 2
Number of favourable outcomes = 8
$$P(\text{difference} = 2) = \frac{8}{36} = \frac{2}{9}$$
Source: Chapter 14, Example 13 (dice outcomes table)
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Explanation
- Always list the sample space systematically using the 6×6 table shown in Example 13. Total outcomes = 36.
- "Difference = 2" means |a − b| = 2, so both (a − b = 2) and (b − a = 2) cases must be counted — students often forget one direction and get 4 instead of 8.
- The pairs are: (1,3),(2,4),(3,5),(4,6),(3,1),(4,2),(5,3),(6,4) — exactly 8.
- Final answer must be in simplest form: $\dfrac{8}{36} = \dfrac{2}{9}$.