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 \[\frac{5}{7}.\]

Options

• Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).

• Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).

• Assertion (A) is true and Reason (R) is false.

• Assertion (A) is false and Reason (R) is true.

Answer 1

Assertion (A) is true and Reason (R) is false.

Explanation:

Step 1 – Assertion: A is true. A leap year has 52 complete weeks and 2 extra days. Sunday is one of those extra days in 2 of the 7 possible cases, so the probability is \[\frac{2}{7}.\]

Step 2 – Reason: R is false. A non-leap year has 52 complete weeks and 1 extra day, so the probability of an extra Sunday and hence 53 Sundays is \[\frac{1}{7},\] not \[\frac{5}{7}.\]