The probability that a leap year, selected at random. will contain 53 Sunday is:

Options

A. `1//7`
B. `2//7`
C. `3//7`
D. `4//7`

Answer

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

### Step-by-Step Solution:

1. **Understand the Total Days in a Leap Year**:
A leap year has a total of 366 days.

**Hint**: Remember that a leap year occurs every four years and has one extra day compared to a common year.

2. **Calculate the Number of Weeks and Extra Days**:
Since there are 7 days in a week, we can calculate the number of complete weeks in 366 days:
\[ \text{Number of weeks} = \frac{366}{7} = 52 \text{ weeks} \text{ and } 2 \text{ extra days} \]
This means there are 52 complete weeks and 2 extra days.

**Hint**: The extra days are important because they determine if we can have an additional Sunday.

3. **Identify the Extra Days**:
The extra days can be any two consecutive days of the week. The possible pairs of extra days are:
- Sunday and Monday
- Monday and Tuesday
- Tuesday and Wednesday
- Wednesday and Thursday
- Thursday and Friday
- Friday and Saturday
- Saturday and Sunday

**Hint**: List all possible combinations of two consecutive days to ensure you don't miss any.

4. **Count the Total Outcomes**:
From the pairs listed, we see that there are a total of 7 possible outcomes (pairs of extra days).

**Hint**: Make sure to count each pair carefully to avoid errors.

5. **Identify Favorable Outcomes**:
Now, we need to find how many of these pairs include Sunday:
- The pairs that include Sunday are:
- Sunday and Monday
- Saturday and Sunday
Thus, there are 2 favorable outcomes.

**Hint**: Focus on the pairs that specifically include Sunday.

6. **Calculate the Probability**:
The probability \( P \) of having 53 Sundays in a leap year is given by the formula:
\[ P(\text{53 Sundays}) = \frac{\text{Favorable outcomes}}{\text{Total outcomes}} = \frac{2}{7} \]

**Hint**: Remember that probability is always calculated as the ratio of favorable outcomes to total outcomes.

### Final Answer:
The probability that a leap year selected at random will contain 53 Sundays is \( \frac{2}{7} \).