Probability Question: What is the chance that two randomly selected people share the same birthday?

Question

Two people are selected at random from a group, assuming that:

• Each day of the year is equally likely to be a birthday.

• There are 365 days in a year (ignoring leap years).

• Birthdays of different people are independent events.

What is the probability that both selected people share the same birthday?

Please provide a clear explanation of the reasoning process or formula used.

Answer 1

0.27

 

Answer 2

The chance that two randomly selected people share the same birthday (ignoring leap years) is:

1 / 365, which is about 0.27%.

This is because once one person’s birthday is fixed, the second person has a 1-in-365 chance of having the same birthday.

Answer 3

The chance that two randomly selected people share the same birthday is about 1 in 365 (0.27%).

Answer 4

 

Person 1: Can have birthday on ANY day → $\frac{365}{365} = 1$

Person 2: Must match Person 1's birthday → $\frac{1}{365}$

Probability both share same birthday:

$$P = 1 \times \frac{1}{365} = \frac{1}{365}$$

Answer: $\frac{1}{365}$