A box contains 90 discs which are numbered 1 to 90. If one disc is drawn at random from the box, find the probability that it bears a :
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Total number of discs = 90
(i) 2-digit numbers less than 40:
2-digit numbers less than 40 are: 10, 11, 12, … , 39 → 30 numbers
$$P = \frac{30}{90} = \frac{1}{3}$$
(ii) Numbers divisible by 5 and greater than 50:
55, 60, 65, 70, 75, 80, 85, 90 → 8 numbers
$$P = \frac{8}{90} = \frac{4}{45}$$
(iii) Perfect square numbers:
1, 4, 9, 16, 25, 36, 49, 64, 81 → 9 numbers
$$P = \frac{9}{90} = \frac{1}{10}$$
Source: Exercise 14.1, Q.18, Chapter 14 – Probability
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Explanation
- Part (i): The 2-digit numbers start from 10. Numbers from 10 to 39 give exactly 30 values (39 − 10 + 1 = 30). Do not include single-digit numbers.
- Part (ii): Multiples of 5 greater than 50 up to 90: start from 55, end at 90 → 8 values. A common mistake is starting from 50 (which is not greater than 50).
- Part (iii): List perfect squares systematically: 1² to 9² all lie within 1–90, giving 9 values. Remember to simplify the fraction.
- Always show the favourable outcomes count clearly before writing the fraction — examiners award method marks for this.