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: Understand the problem:
We are asked to find the probability that two friends, born in the year 2000, have the same birthday. We will assume that the birthdays of the two friends are independent and that each day of the year is equally likely for both of them.

Step 2: Total possible outcomes:
Since the year 2000 is a leap year, there are 366 days in the year. The first friend can have their birthday on any of the 366 days.
For the second friend, there are 366 possible days for their birthday as well, but we are interested in the case where they share the same birthday.

Step 3: Favorable outcome:
For the two friends to have the same birthday, the second friend must have the same birthday as the first. There is exactly 1 favorable outcome for the second friend's birthday — it must match the first friend's birthday.

Step 4: Probability calculation:
The probability that the second friend has the same birthday as the first friend is the ratio of favorable outcomes to total possible outcomes.
Thus, the probability is: \[ P(\text{same birthday}) = \frac{1}{366} \]

Conclusion:
The probability that the two friends have the same birthday is \( \boxed{\frac{1}{366}} \).