CBSE2026Class Class 10 · Mathematics1 Marks · Long✅ Verified
Assertion (A): The probability that a leap year has 53 Mondays is $\frac{2}{7}$. Reason (R): The probability that a non-leap year has 53 Mondays is $\frac{5}{7}$. Choose the correct option: (a) Both A and R are true and R is the correct explanation of A. (b) Both A and R are true, but R is not the correct explanation of A. (c) A is true, but R is false. (d) A is false, but R is true.
✅ Answer & Solution
A leap year has 366 days = 52 weeks + 2 extra days. The 2 extra days can be any of 7 pairs: (Sun-Mon), (Mon-Tue), (Tue-Wed), (Wed-Thu), (Thu-Fri), (Fri-Sat), (Sat-Sun). Out of these, 2 pairs contain Monday, so $P(53 \text{ Mondays}) = \frac{2}{7}$, making Assertion (A) true. A non-leap year has 365 days = 52 weeks + 1 extra day, which can be any of the 7 days with equal probability $\frac{1}{7}$ each, so $P(53 \text{ Mondays in non-leap year}) = \frac{1}{7}$, NOT $\frac{5}{7}$. Hence Reason (R) is false. Correct option: (c) A is true, R is false.
