The probability that a leap year selected ar random contains either 53 sundays or 53 mondays, 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 contains either 53 Sundays or 53 Mondays, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Structure of a Leap Year**:
A leap year has 366 days. This can be divided into 52 weeks and 2 extra days. Therefore, in any leap year, there are definitely 52 Sundays and 52 Mondays.

2. **Identify the Extra Days**:
Since there are 2 extra days in a leap year, we need to determine what these days can be. The possible combinations of the 2 extra days are:
- Sunday and Monday
- Monday and Tuesday
- Tuesday and Wednesday
- Wednesday and Thursday
- Thursday and Friday
- Friday and Saturday
- Saturday and Sunday

3. **Count the Total Outcomes**:
From the combinations listed above, we can see that there are a total of 7 possible outcomes for the 2 extra days.

4. **Determine Favorable Outcomes**:
We need to find the combinations that result in either 53 Sundays or 53 Mondays:
- The combination "Sunday and Monday" gives us 53 Sundays and 53 Mondays.
- The combination "Saturday and Sunday" gives us 53 Sundays.
- The combination "Monday and Tuesday" gives us 53 Mondays.

Therefore, the favorable outcomes are:
- Sunday and Monday
- Saturday and Sunday
- Monday and Tuesday

This gives us a total of 3 favorable outcomes.

5. **Calculate the Probability**:
The probability (P) of having either 53 Sundays or 53 Mondays is given by the formula:
\[ P = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{3}{7} \]

### Final Answer:
The probability that a leap year selected at random contains either 53 Sundays or 53 Mondays is \(\frac{3}{7}\).