Question

Ram and Syam are friends. Probability that both will have same birthday is:

• A. \( \frac{364}{365} \)
• B. \( \frac{1}{365} \)
• C. \( \frac{1}{364} \)
• D. \( \frac{363}{365} \)

Hint:

The probability that two people will have the same birthday is \( \frac{1}{365} \), but for both to have the same birthday, consider that one person’s birthday is already fixed.

Answer 1

The Correct Option is A

Step 1: Understanding the Probability.
There are 365 days in a year (ignoring leap years), and each person has an equal chance of being born on any of these days. For the probability that Ram and Syam will have the same birthday, the first person (Ram) can have his birthday on any of the 365 days, but for Syam to have the same birthday, he must be born on the same day as Ram. 
Step 2: Probability Calculation.
The probability that Syama's birthday matches Rama's birthday is: \[ P(\text{same birthday}) = \frac{1}{365} \] However, for both to have the same birthday, the event happens only after considering the first personas (Ram's) birthday choice, so the probability is \( \frac{364}{365} \) for Syam. 
Step 3: Conclusion.
Thus, the probability that both Ram and Syam will have the same birthday is: \[ P(\text{same birthday}) = \frac{364}{365} \]