What is the probability that a leap year selected at random will contain either 53 Thursdays
or Friday?

To solve this problem, we need to determine the probability that a randomly selected leap year contains either 53 Thursdays or 53 Fridays.

### Key Points:
1. **Leap Year Details**: 
   - A leap year has 366 days.
   - It consists of 52 weeks (364 days) plus 2 extra days.

2. **Distribution of Days**:
   - In a leap year, those extra 2 days can be any of the following combinations:
     - (Sunday, Monday)
     - (Monday, Tuesday)
     - (Tuesday, Wednesday)
     - (Wednesday, Thursday)
     - (Thursday, Friday)
     - (Friday, Saturday)
     - (Saturday, Sunday)

3. **Event Analysis**:
   - For there to be 53 Thursdays, one of the two extra days must be a Thursday.
   - Similarly, for there to be 53 Fridays, one of the two extra days must be a Friday.

### Step-by-Step Calculation:
- **Total Outcomes**: There are 7 possible combinations of the two extra days.
- **Favorable Outcomes**:
  - To have 53 Thursdays, the extra days can be (Wednesday, Thursday) or (Thursday, Friday).
  - To have 53 Fridays, the extra days can be (Thursday, Friday) or (Friday, Saturday).

  The favorable combinations are:
  - (Wednesday, Thursday) (for 53 Thursdays)
  - (Thursday, Friday) (for both 53 Thursdays and 53 Fridays)
  - (Friday, Saturday) (for 53 Fridays)

  Thus, there are 3 favorable combinations out of the 7 possible ones.

### Probability Calculation:
- The probability that a leap year contains either 53 Thursdays or 53 Fridays is:

\[
\text{Probability} = \frac{\text{Number of Favorable Outcomes}}{\text{Total Possible Outcomes}} = \frac{3}{7}
\]

So, the probability is \(\frac{3}{7}\).

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Would you like to go over any details or have any questions?

Here are some related questions you might find interesting:
1. What is the probability of getting 53 Sundays in a leap year?
2. How does the probability differ in a non-leap year?
3. What is the probability that a leap year contains 53 Saturdays?
4. If a year is selected at random, what is the probability that it is a leap year?
5. How would the calculation change if we were interested in exactly 53 Thursdays, without considering Fridays?

**Tip**: Understanding how to break down the problem into possible outcomes can simplify probability calculations!

Understand the probability of a leap year containing either 53 Thursdays or 53 Fridays. Learn the calculations involving leap year structure and days distribution, with step-by-step explanations. Suitable for students in Grades 10-12.

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