Assertion (A) : The probability that a leap year has 53 Sundays is $\dfrac{2}{7}$.
Reason (R) : The probability that a non-leap year has 53 Sundays is $\dfrac{5}{7}$.
Choose the correct option :
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
(c) Assertion (A) is true but Reason (R) is false.
A leap year has 366 days = 52 weeks + 2 extra days. The 2 extra days can be any of 7 pairs; 2 pairs include Sunday, so P(53 Sundays) = 2/7. ✓
A non-leap year has 365 days = 52 weeks + 1 extra day. Only 1 of 7 days can be Sunday, so P(53 Sundays) = 1/7, not 5/7. ✗
Source: Chapter 14, Probability — Theoretical Approach
Explanation
- Assertion is correct: leap year gives 2 extra days, and exactly 2 of the 7 possible pairs (Sat–Sun, Sun–Mon) contain a Sunday → P = 2/7.
- Reason is wrong: a non-leap year gives only 1 extra day; P(53 Sundays) = 1/7, not 5/7. (5/7 would be the probability of not getting a 53rd Sunday in a non-leap year... even that is 6/7, so 5/7 is simply incorrect.)
- Examiners expect you to justify both A and R briefly — don't just state the option.