What is the chance that a non leap year , selected at random , will contain 53 Sunday ?

Answer

To solve the problem of finding the chance that a non-leap year selected at random will contain 53 Sundays, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of a Non-Leap Year**:
A non-leap year has a total of 365 days.

2. **Calculate the Number of Weeks**:
Since there are 7 days in a week, we can calculate the number of complete weeks in 365 days:
\[ \text{Number of weeks} = \frac{365}{7} = 52 \text{ weeks} \text{ and } 1 \text{ extra day} \]
This means there are 52 complete weeks and 1 extra day.

3. **Determine the Number of Sundays**:
In 52 weeks, there are 52 Sundays. The extra day can be any day of the week (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, or Sunday).

4. **Identify the Favorable Outcome**:
For a non-leap year to have 53 Sundays, the extra day must be a Sunday.

5. **Calculate the Total Possible Outcomes**:
The extra day can be any one of the 7 days of the week. Thus, the total possible outcomes for the extra day are 7.

6. **Calculate the Probability**:
The probability of the extra day being a Sunday (which would give us 53 Sundays in total) is:
\[ P(\text{53 Sundays}) = \frac{\text{Number of favorable outcomes}}{\text{Total possible outcomes}} = \frac{1}{7} \]

### Final Answer:
The probability that a non-leap year selected at random will contain 53 Sundays is \(\frac{1}{7}\).

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