RE: What's the probability that 3 out of 23 people will share the same birthday?
January 21, 2022 at 6:32 am
(This post was last modified: January 21, 2022 at 6:45 am by Jehanne.)
Yes, there is a general formula, which can be reasoned as follows:
1) The probability of an event plus its complement (the event not occurring) is 1 (or, "unity").
2) While not being entirely true, we may assume, for convenience, that every day of the year is equally likely to be born on.
3) The probability of being born on any one day is 1/365 for non-leap years.
4) If a single person is born on one day, there are 364 other days for another individual to be born on, such that the two individuals do not have the same birthday. For the third individual, there would be 363 days, etc.
5) 1 - (365 * 364 * 363...) / 365 ^ n would give the probability that 2 or more individuals would have the same birthday.
P.S. Okay, it's 4 AM, and, so, I misread your question a bit. Yes, getting the probability for exactly three individuals is quite a bit more tricky.
1) The probability of an event plus its complement (the event not occurring) is 1 (or, "unity").
2) While not being entirely true, we may assume, for convenience, that every day of the year is equally likely to be born on.
3) The probability of being born on any one day is 1/365 for non-leap years.
4) If a single person is born on one day, there are 364 other days for another individual to be born on, such that the two individuals do not have the same birthday. For the third individual, there would be 363 days, etc.
5) 1 - (365 * 364 * 363...) / 365 ^ n would give the probability that 2 or more individuals would have the same birthday.
P.S. Okay, it's 4 AM, and, so, I misread your question a bit. Yes, getting the probability for exactly three individuals is quite a bit more tricky.
