People share the same birthday

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!!!


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