Solve the following questions.
Find the probability of getting 53 Fridays in a year.

Answer

To find the probability of getting 53 Fridays in a year, we need to consider both normal years and leap years. Let's break down the solution step by step:

### Step-by-Step Solution

1. **Understand the Number of Days in a Year:**
- A normal year has **365 days**.
- A leap year has **366 days**.

2. **Calculate the Number of Weeks:**
- In a normal year (365 days), there are **52 complete weeks** (52 weeks × 7 days = 364 days).
- This leaves **1 extra day** (365 - 364 = 1).
- In a leap year (366 days), there are also **52 complete weeks** (52 weeks × 7 days = 364 days).
- This leaves **2 extra days** (366 - 364 = 2).

3. **Determine Fridays in a Normal Year:**
- In a normal year, there are **52 Fridays** from the 52 weeks.
- The extra day can be any day of the week (Sunday, Monday, Tuesday, Wednesday, Thursday, Friday, or Saturday).
- The probability that this extra day is a Friday is:
\[ P(\text{53 Fridays in a normal year}) = \frac{1}{7} \]

4. **Determine Fridays in a Leap Year:**
- In a leap year, there are still **52 Fridays** from the 52 weeks.
- The two extra days can be any combination of two consecutive days of the week.
- The possible combinations of the extra days are:
- Sunday and Monday
- Monday and Tuesday
- Tuesday and Wednesday
- Wednesday and Thursday
- Thursday and Friday (includes a Friday)
- Friday and Saturday (includes a Friday)
- Saturday and Sunday
- Out of these combinations, **2 combinations** (Thursday & Friday, and Friday & Saturday) include a Friday.
- Therefore, the probability that at least one of the two extra days is a Friday is:
\[ P(\text{53 Fridays in a leap year}) = \frac{2}{7} \]

5. **Final Summary:**
- For a normal year, the probability of getting 53 Fridays is \( \frac{1}{7} \).
- For a leap year, the probability of getting 53 Fridays is \( \frac{2}{7} \).