The probability that the `13^(th)` day of any randomly chosen month is a second Saturday, is (A) `1/7` (B) `1/12` (C) `1/84` (D) `19/84`

Options

A. `1//7`
B. `1//12`
C. `1//84`
D. `19//84`

Answer

To solve the problem, we need to find the probability that the 13th day of a randomly chosen month is a second Saturday.

### Step-by-Step Solution:

1. **Understanding the Problem**:
- We need to determine the probability that the 13th day of a month is the second Saturday of that month.

2. **Choosing a Month**:
- There are 12 months in a year. When we randomly choose a month, the probability of choosing any specific month is:
\[ P(\text{Choosing a month}) = \frac{1}{12} \]

3. **Identifying the Condition for the 13th Day**:
- For the 13th day to be the second Saturday, the first Saturday must be on the 6th day of the month. This means that if the 6th is a Saturday, then the 13th will also be a Saturday.

4. **Calculating the Probability of the 6th Being a Saturday**:
- There are 7 days in a week, and any day of the week is equally likely to be the first day of the month. Therefore, the probability that the 6th day of the month is a Saturday is:
\[ P(\text{6th is Saturday}) = \frac{1}{7} \]

5. **Combining the Probabilities**:
- The overall probability that the 13th is a second Saturday is the product of the probability of choosing a month and the probability that the 6th day is a Saturday:
\[ P(\text{13th is second Saturday}) = P(\text{Choosing a month}) \times P(\text{6th is Saturday}) = \frac{1}{12} \times \frac{1}{7} = \frac{1}{84} \]

6. **Final Answer**:
- Thus, the probability that the 13th day of any randomly chosen month is a second Saturday is:
\[ \frac{1}{84} \]
- The correct option is (C) \( \frac{1}{84} \).