Assertion (A): The probability that a leap year has 53 Sundays is $\frac{2}{7}$.

Reason (R): The probability that a non-leap year has 53 Sundays is $\frac{5}{7}$.

Question

Assertion (A): The probability that a leap year has 53 Sundays is $\frac{2}{7}$.

Reason (R): The probability that a non-leap year has 53 Sundays is $\frac{5}{7}$.

Accepted Answer

Step 1: A leap year has 366 days = 52 weeks + 2 extra days. P(53 Sundays) $= \frac{2}{7}$, so Assertion is true. A non-leap year has 365 days = 52 weeks + 1 extra day. P(53 Sundays) $= \frac{1}{7}$, not $\frac{5}{7}$, so Reason is false.

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