The probability that a non-leap year has 53 Sundays, is :

Question

Accepted Answer

In a non-leap year, there are 365 days. To determine the probability that a non-leap year has 53 Sundays, we need to consider how the days of the week are distributed over the year.

1. **Days in a Non-Leap Year:**
   - A non-leap year has 365 days.
   - 365 days can be divided into 52 weeks and 1 extra day (since 365 = 52 * 7 + 1).

2. **Distribution of Days:**
   - In a non-leap year, there are 52 complete weeks, which means there are 52 Sundays.
   - The extra day can be any day of the week: Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, or Saturday.

3. **Probability of the Extra Day Being a Sunday:**
   - There are 7 possible days that the extra day can be.
   - For there to be 53 Sundays in a non-leap year, the extra day must be a Sunday.
   - Therefore, the probability that the extra day is a Sunday is $\frac{1}{7}$.

4. **Explanation of Options:**
   - **Option 1 ($\frac{2}{7}$):** This would imply that there are two favorable outcomes for the extra day being a Sunday, which is incorrect since there is only one extra day.
   - **Option 2 ($\frac{5}{7}$):** This suggests that five out of the seven days could be Sundays, which is not possible as there is only one extra day.
   - **Option 3 ($\frac{6}{7}$):** This implies that six out of the seven days could be Sundays, which is incorrect for the same reason as above.
   - **Option 4 ($\frac{1}{7}$):** This correctly represents the probability that the extra day is a Sunday, as there is only one favorable outcome (the extra day being a Sunday) out of seven possible outcomes.

Therefore, the correct answer is Option 4, $\frac{1}{7}$, as it accurately reflects the probability that a non-leap year will have 53 Sundays.