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

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

1. Assertion (A) is true, but Reason (R) is false.

2. Assertion (A) is false, but Reason (R) is true.

3. Both Assertion (A) and Reason (R) are correct, and Reason (R) is the correct reason for Assertion (A).

4. Both Assertion (A) and Reason (R) are correct, and Reason (R) is incorrect reason for Assertion (A).

In a leap year, there are 366 days.

366 days = 52 weeks + 2 days

These 2 days can be (Mon, Tue), (Tue, Wed), (Wed, Thu), (Thu, Fri), (Fri, Sat), (Sat, Sun), and (Sun, Mon).

Total number of possible outcomes = 7

Number of favourable outcomes (Getting Sunday as one of the extra days) = 2 (i.e., (Sat, Sun), (Sun, Mon)).

P(Getting Sunday as one of the extra days) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{2}{7}$

∴ Assertion (A) is true.

In a non - leap year, there are 365 days.

365 days = 52 weeks + 1 days

These 1 days can be Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday.

Total number of possible outcomes = 7

Number of favourable outcomes (Getting Sunday as one of the extra days) = 1

P(Getting Sunday as one of the extra days) = $\dfrac{\text{No. of favourable outcomes}}{\text{No. of possible outcomes}} = \dfrac{1}{7}$

∴ Reason (R) is false.

∴ Assertion (A) is true, but Reason (R) is false.

Hence, option 1 is the correct option.