Probability Maths Question

[rosamundjohn]

There are 20 people in a meeting.
What is the probability that 2 of these people have the same birthday? not same year just same day.

[woofgang]

do you mean day of the month or day of the week that year? Are they all the same age? Ie born in the same year?

[bibblebub]

you only need 23 (as far as i remember) for there to be >50% that 2 of them will share a birthday, and you can work that out by calculating the probability that none of them share the same day

[jim360]

It's about 40%, I think, if I remember of the top of my head. The simplest way to work out the answer is to calculate the probability that no two people share the same birthday, ie all are different. This is equal to the following (ignoring leap years):

P(all different birthdays) = (365/365)*(364/365)*(363/365)*(362/365)*...*(347/365)*(346/365) = about 0.589.

We want one minus this, as we've worked out the probability only that no-one shares the same birthday, so we have:

P(two share birthday) = 1-0.5885... = 0.4114...

So there is a 41% chance that at least two people share the same birthday. This isn't quite what your posts implies the question was, but calculating the probability that exactly two people share the same birthday is rather trickier so I'm guessing that it means "at least two".

[jim360]

The above assumes that there is an equal chance that anyone is born on a particular day, but I believe statistically that this isn't the case, and that certain days see more babies than others. So the above is a crude model only.

[Peter Pedant]

Bibbz is right
and Me is wrong - ok is not following the standard analysis
which is.....
two epople not sharing..... 364/365

three people not sharing 364/365 times 363/365

and so on down to 20

and the fraction 365.364.363......./ 365 to power 20

is around a half