# 30 people, 365 days, birthday

• Nov 22nd 2011, 03:25 AM
metlx
30 people, 365 days, birthday
There is 30 people in a group (29 + you).
What's the probabillity that one of them has the exact same birthday as you?

This is what I've got thus far. I have no idea how to check if it's correct though.

30 * (1/365)^1 * (364/365)^29 = 0.076 = 7.6%
• Nov 22nd 2011, 04:53 AM
metlx
Re: 30 people, 365 days, birthday
Year doesn't matter. Just days in the year.
• Nov 22nd 2011, 06:34 AM
Soroban
Re: 30 people, 365 days, birthday
Hello, metlx!

Quote:

There are 30 people in a group (29 + you).
What's the probabillity that one of them has the exact same birthday as you?

This is what I've got thus far.
I have no idea how to check if it's correct though.

30 * (1/365)^1 * (364/365)^29 = 0.076 = 7.6%

. . Your answer was:.$\displaystyle 0.075905885 \:\approx\: 7.6\%$
But miraculously, you came out very close to the correct answer.

If you want the probability that exactly one has your birthday,

. . the probability is:.$\displaystyle {29\choose1}\left(\frac{1}{365}\right)\left(\frac{ 364}{365}\right)^{28} \:=\:0.07357727 \:\approx\:7.4\%$

If you want the probability that at least one has your birthday . . .

The probability that no one has your birthday is:
. . $\displaystyle \left(\frac{364}{365}\right)^{29} \:=\:0.923521598 \:\approx\:92.4\%$

Therefore, the probability that at least one has your birthday is:
. . . . . $\displaystyle 1 - 92.4\% \;=\;7.6\%$