In a room filled with 370 people will there be at least two people who celebrate their birthdays on the same day?

Answer 1

Yes, in a room filled with 370 people, there will be at least two people who celebrate their birthdays on the same day. This is known as the birthday paradox, a phenomenon in probability theory where the probability of two people sharing a birthday becomes surprisingly high even with a relatively small group of people. The formula to calculate the probability of at least two people sharing a birthday in a group is 1 - (365!/((365-n)! * 365^n)), where n is the number of people in the group.

Answer 2

(Please note that this is interpreted to be "ANY two people with ANY birthdate the same".) Yes, even if they "celebrate" their common birthday on some other day. In fact you only need 367. A random selection of people will have several pairs who share the same birthday, and several dates (especially the magic "February 29") are almost certain to be omitted. Statistical probability requires a very large sample, so that if 365,000 people were polled, you would have close to 1000 of each separate date, and as many as 250 with February 29th. (a 1-in-1461 average).