"Eight Ball" is a game played on a pool table with 15 balls numbered 1 to 15 and a "cue ball" that is solid and white. Of the 15 numbered balls, eight are solid (non-white) coloured and numbered 1 to 8 and seven are striped balls numbered 9 to 15.
The 15 numbered pool balls (no cue ball) are placed in a large bowl and mixed, then one ball is drawn out at random.
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding stimulus
Model Answer
Total number of balls = 15
(i) Only one ball bears number 8.
$$P(\text{ball numbered 8}) = \frac{1}{15}$$
(ii) Even-numbered balls from 1 to 15: 2, 4, 6, 8, 10, 12, 14 → 7 balls
$$P(\text{even number}) = \frac{7}{15}$$
(iii) Solid coloured balls are numbered 1 to 8. Even numbers among these: 2, 4, 6, 8 → 4 balls
$$P(\text{solid and even}) = \frac{4}{15}$$
Source: Probability (Case Study based on pool ball problem)
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Explanation
- Total outcomes = 15 (only numbered balls, cue ball excluded).
- For (ii), list all even numbers up to 15 carefully — students often miss that 7 even numbers exist (2,4,6,8,10,12,14).
- For (iii), restrict to solid balls (1–8) first, then pick even ones (2,4,6,8) = 4. Do not include striped even numbers (10,12,14) here.
- Write the favourable outcomes explicitly before writing the fraction — examiners award step marks.