Find the probability that 5 Sundays occur in the month of November of a randomly selected year.

Answer

To find the probability that there are 5 Sundays in the month of November of a randomly selected year, we can follow these steps:

### Step 1: Understand the structure of November
November has 30 days. Since a week has 7 days, we can calculate how many complete weeks are in November and how many extra days there are.

**Hint:** Remember that 30 days can be divided into weeks to find the number of complete weeks and leftover days.

### Step 2: Calculate the number of complete weeks and extra days
30 days can be divided into 4 complete weeks (which is 28 days) and there will be 2 extra days left over.

**Hint:** Use division to find how many weeks fit into 30 days and then find the remainder.

### Step 3: Identify the possible scenarios for the extra days
The extra 2 days can be any combination of the days of the week. They can be:
- Sunday and Monday
- Monday and Tuesday
- Tuesday and Wednesday
- Wednesday and Thursday
- Thursday and Friday
- Friday and Saturday
- Saturday and Sunday

**Hint:** List all combinations of 2 consecutive days starting from Sunday.

### Step 4: Determine the favorable outcomes for having 5 Sundays
For November to have 5 Sundays, one of the extra days must be a Sunday. The favorable outcomes are:
1. Sunday and Monday
2. Saturday and Sunday

Thus, there are 2 favorable outcomes.

**Hint:** Think about which combinations include Sunday.

### Step 5: Calculate the total outcomes
Since there are 7 days in a week, the total possible outcomes for the extra days are 7.

**Hint:** Count the total combinations of 2 consecutive days in a week.

### Step 6: Calculate the probability
The probability \( P \) of having 5 Sundays in November can be calculated using the formula:
\[ P = \frac{\text{Number of favorable outcomes}}{\text{Total outcomes}} = \frac{2}{7} \]

**Hint:** Use the formula for probability which is favorable outcomes divided by total outcomes.

### Final Answer
The probability that there are 5 Sundays in the month of November of a randomly selected year is \( \frac{2}{7} \).