**Question: **What are the chances that at least two out of a group of fifty people share the same birthday?

**Answer:**

Probability of atleast two share the same birthday = 1 - probability of all 50 have different birthdays

Probability of all 50 have different birthday

= 365/365 * 364/365 * 363/365 * ... * 317/365 * 316/365

= (365 * 364 * 363 * 362 * ... * 317 * 316)/36550

= 0.0296264

Probability of atleast two share the same birthday

= 1 - 0.0296264

= 0.9703735

= 97% approx.

Thus, the probability of atleast two out of a group of 50 people share the same birthday is 97%

This explains why in a school/college with classrooms of 50 students, there are at least two students with a birthday on the same day of the year. Also, if there are 23 people in the room, then there are 50% chances that atleast two of them have a birthday on the same day of the year!!!