A bag contains 30 balls out of which '$m$' number of balls are blue in colour.
Generated by claude-sonnet-4-6 · 2026-06-15 10:28 · grounding rag
Model Answer
(i)
Total balls = 30, blue balls = $m$
$$P(\text{blue}) = \frac{m}{30}$$
$$P(\text{not blue}) = 1 - \frac{m}{30} = \frac{30 - m}{30}$$
(ii)
After adding 6 blue balls: total balls = 36, blue balls = $m + 6$
$$P(\text{blue after adding}) = \frac{m+6}{36}$$
Given condition:
$$\frac{m+6}{36} = \frac{5}{4} \times \frac{m}{30}$$
$$\frac{m+6}{36} = \frac{m}{24}$$
$$24(m+6) = 36m$$
$$24m + 144 = 36m$$
$$12m = 144$$
$$\boxed{m = 12}$$
Source: Chapter 14, Section 14.1
---
Explanation
- (i) uses the complementary event formula: $P(\bar{E}) = 1 - P(E)$. Leave answer in terms of $m$.
- (ii) Set up the equation directly from the given condition, cross-multiply, and solve. Show every algebraic step — examiners award marks for working, not just the final answer. Verify: $P_1 = 12/30 = 2/5$; $P_2 = 18/36 = 1/2 = (5/4)(2/5)$ ✓