Question

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 $\frac{5}{7}$.

• A. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).
• B. Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).
• C. Assertion (A) is true, but Reason (R) is false.
• D. Assertion (A) is false, but Reason (R) is true.

Hint:

For any day of the week (Monday, Tuesday, etc.):
- Probability of 53 occurrences in a leap year is always $\frac{2}{7}$.
- Probability of 53 occurrences in a non-leap year is always $\frac{1}{7}$.
Memorizing these two standard fractions will save you from drawing out sample spaces in exams!

Answer 1

The Correct Option is C

Step 1: Recall the two standard results for this classic problem.
For any fixed weekday, the probability of it occurring 53 times in a leap year is always $\frac27$, and in a non-leap year it is always $\frac17$.
Step 2: Check Assertion (A) against the standard result.
A claims the probability of 53 Mondays in a leap year is $\frac27$, which matches the standard result exactly, so A is true.
Step 3: Check Reason (R) against the standard result.
R claims the probability of 53 Mondays in a non-leap year is $\frac57$, but the correct value is $\frac17$, so R is false.
\[ \boxed{\text{Option (C): A is true, R is false}} \]