What is the probability of two persons being born on the same day (ignoring date)?

Options

A. `1//49`
B. `1//365`
C. `1//7`
D. `2//7`

Answer

To find the probability of two persons being born on the same day of the week, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Total Days in a Week**:
- There are 7 days in a week (Monday, Tuesday, Wednesday, Thursday, Friday, Saturday, Sunday).

2. **Determine the Total Outcomes**:
- For two persons (let's call them A and B), each can be born on any of the 7 days.
- Therefore, the total number of outcomes for the days on which both A and B can be born is:
\[ \text{Total Outcomes} = 7 \times 7 = 49 \]

3. **Identify Favorable Outcomes**:
- The favorable outcomes are the scenarios where both A and B are born on the same day.
- There are 7 favorable outcomes (both can be born on Monday, both on Tuesday, and so on for each day of the week).

4. **Calculate the Probability**:
- The probability \( P \) of both persons being born on the same day is given by the formula:
\[ P(\text{same day}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{7}{49} \]
- Simplifying this gives:
\[ P(\text{same day}) = \frac{1}{7} \]

### Final Answer:
The probability of two persons being born on the same day is \( \frac{1}{7} \).