What is the probability that in a group of two people, both will have the same birthday, assuming that there are 365 days in a year and no one has his/her birthday on 29th Fabruary ?

Answer

To solve the problem, we need to calculate the probability that two people have the same birthday, given that there are 365 days in a year.

### Step-by-Step Solution:

1. **Identify the Total Outcomes**:
- Each person can have their birthday on any of the 365 days.
- Therefore, for two people, the total number of outcomes is:
\[ \text{Total Outcomes} = 365 \times 365 = 365^2 \]

2. **Identify the Favorable Outcomes**:
- We want both people to have the same birthday. If person A has a birthday on any one of the 365 days, person B must have their birthday on the same day.
- Thus, there are 365 favorable outcomes (one for each day of the year).

3. **Calculate the Probability**:
- The probability \( P \) that both people have the same birthday is given by the ratio of the number of favorable outcomes to the total outcomes:
\[ P(\text{same birthday}) = \frac{\text{Number of Favorable Outcomes}}{\text{Total Outcomes}} = \frac{365}{365^2} \]
- Simplifying this, we get:
\[ P(\text{same birthday}) = \frac{1}{365} \]

### Final Answer:
The probability that both people have the same birthday is \( \frac{1}{365} \).

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