What is the probability that a leap year has 53 Sundays ?

Explanation

To find the probability that a leap year has 53 Sundays, we can follow these steps:

### Step 1: Understand the structure of a leap year
A leap year has 366 days. Since there are 7 days in a week, we can determine how many complete weeks are in a leap year.

**Calculation:**
- Number of weeks in a leap year = 366 days ÷ 7 days/week = 52 weeks and 2 extra days.

### Step 2: Identify the extra days
In a leap year, after accounting for the 52 complete weeks, there are 2 extra days. These extra days can be any combination of the days of the week.

### Step 3: List the possible combinations of the extra days
The two extra days can be:
1. Sunday and Monday
2. Monday and Tuesday
3. Tuesday and Wednesday
4. Wednesday and Thursday
5. Thursday and Friday
6. Friday and Saturday
7. Saturday and Sunday

### Step 4: Determine favorable outcomes for having 53 Sundays
To have 53 Sundays in a leap year, one of the extra days must be a Sunday. The combinations that include Sunday are:
- Sunday and Monday
- Saturday and Sunday

Thus, there are 2 favorable outcomes (Sunday and Monday, Saturday and Sunday).

### Step 5: Calculate the total outcomes
The total possible combinations of the two extra days are 7 (as listed in Step 3).

### Step 6: Calculate the probability
The probability \( P \) of having 53 Sundays in a leap year is given by the formula:

\[ P(\text{53 Sundays}) = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{7} \]

### Final Answer
The probability that a leap year has 53 Sundays is \( \frac{2}{7} \).

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