Question

Two friends were born in the year 2000. The probability that they have the same birthday is :

• A. $\frac{1}{365}$
• B. $\frac{364}{365}$
• C. $\frac{1}{366}$
• D. $\frac{365}{366}$

Answer 1

The Correct Option is C

Step 1: Understanding the problem:
We are asked to find the probability that two friends born in the year 2000 have the same birthday.
In a leap year (like 2000), there are 366 days. Assuming that each day is equally likely for a birthday, we need to calculate the probability that two people have the same birthday.

Step 2: Probability calculation:
The first person can have their birthday on any of the 366 days, so there is no restriction on their birthday.
For the second person to have the same birthday, they must have their birthday on the same day as the first person.
The probability of this happening is: \[ \frac{1}{366} \] because there is only 1 favorable outcome (the same birthday) out of 366 possible outcomes (the 366 days of the leap year).

Step 3: Conclusion:
Thus, the probability that the two friends have the same birthday in a leap year is \(\frac{1}{366}\).