In the following question, A statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as.
Assertion (A): The probability that a non - leap year has 53 Sundays is `1/7`.
Reason (R): In a year we have 52 complete weeks which means 364 days and 1 day extra.

Options

A. Both A and R are true and R is the correct explanation for A.
B. Both A and R are true and R is not correct explanation for A.
C. A is true but R is false.
D. A is false but R is true.

Answer

To solve the question, we need to analyze the Assertion (A) and the Reason (R) provided.

### Step 1: Understand the Assertion
The assertion states that "The probability that a non-leap year has 53 Sundays is \( \frac{1}{7} \)".

- A non-leap year has 365 days.
- In a week, there are 7 days.
- When we divide 365 by 7, we get 52 complete weeks (which accounts for 364 days) and 1 extra day.

### Step 2: Analyze the Reason
The reason states that "In a year we have 52 complete weeks which means 364 days and 1 day extra".

- This is true because \( 365 = 52 \times 7 + 1 \).
- Therefore, there are indeed 52 complete weeks and 1 extra day.

### Step 3: Determine the Probability of 53 Sundays
Now, we need to determine the probability of having 53 Sundays in a non-leap year.

- Since there are 52 complete weeks, there are 52 Sundays.
- The extra day can be any day of the week (Sunday, Monday, Tuesday, etc.).
- Thus, there are 7 possible outcomes for the extra day.
- Only one of these outcomes (the extra day being a Sunday) will result in having 53 Sundays.

The probability \( P \) of having 53 Sundays is given by:
\[ P(\text{53 Sundays}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{1}{7} \]

### Step 4: Conclusion
Both the assertion and the reason are true, and the reason correctly explains the assertion.

### Final Answer
- Assertion (A) is TRUE.
- Reason (R) is TRUE.
- The reason is a correct explanation of the assertion.