Two friends Anil and Ashraf were born in the December month in the year 2010. Find the probability that :
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
December has 31 days, so the total number of possible dates of birth = 31.
(i) Probability that they share the same date of birth:
Favourable outcomes = 31 (Anil can be born on any of 31 dates; Ashraf's birthday matches if born on that same date)
$$P(\text{same date}) = \frac{31}{31 \times 31} = \frac{1}{31}$$
(ii) Probability that they have different dates of birth:
$$P(\text{different dates}) = 1 - P(\text{same date}) = 1 - \frac{1}{31} = \frac{30}{31}$$
Source: Chapter 14, Section 14.1 — Probability: A Theoretical Approach
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Explanation
- December has 31 days, so each person can be born on any of 31 dates. Total equally likely outcomes for the pair = 31 × 31 = 961.
- Favourable outcomes for the same date = 31 (any matching pair like 1–1, 2–2, … 31–31).
- For part (ii), use the complementary event rule: P(different) = 1 − P(same). This is the standard method as shown in Example 6 of the chapter.