Q1. [1] § Chapter Opening and Epigraph § 14.1 Probability — A Theoretical Approach § 14.2 Summary
If a digit is chosen at random from the digits 1, 2, 3, 4, 5, 6, 7, 8, 9; then the probability that this digit is an odd prime number is :
- A $\dfrac{1}{3}$
- B $\dfrac{2}{3}$
- C $\dfrac{4}{9}$
- D $\dfrac{5}{9}$
Previously asked in CBSE board exam
2024 30/3/1 Q15
Generated by claude-sonnet-4-6 · 2026-06-15 10:29 · grounding rag
Model Answer
Option A: $\dfrac{1}{3}$
Total outcomes = 9. Odd prime numbers from 1–9 are: 3, 5, 7 → 3 favourable outcomes.
$$P(\text{odd prime}) = \frac{3}{9} = \frac{1}{3}$$
Explanation
Note that 1 is not a prime number, and 2 is the only even prime (not odd). So odd primes in {1,2,…,9} are only 3, 5, 7 — giving 3 favourable outcomes out of 9. A common mistake is including 1 or 2, which would change the answer.
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