#17: How many people do I need to have at my birthday party so that there is a better-than-even chance that one of them will share my birthday i.e. 17/12??…

Q: How many people do I need to have at my birthday party so that there is a better-than-even chance that one of them will share My birthday??…

Now our problem here is a bit different…

A: Disregarding leap years, there are 365 possible birthdays, so there’s a 1 in 365 chance that any random person will have the same birthday as mine.

However, there’s not quite a 2 in 365 chance that at least one of two randomly invited persons will have the same birthday as mine. That chance is actually 1 – (364/365)^2 (that is, the complement of the chance that both of the two people have a different birthday from mine) which is just slightly less than 2/365.

If I invite 4 guests, the chance will be about 0,01091 = 1.091% that one or more will have the same birthday as mine. That’s the closest I can get to a 1% chance.

To get closest to a 10% chance I have to invite more than 36.5 people (and how do I invite half a person anyhow?) Inviting 37 people gives me a 9.653% chance (1 – (364/365)^37) but 38 people gets me closest, with a 9.900% chance.

To get closest to a 50% chance I have to invite 253 people. (50.048% chance)!!…