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%

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- Nov 22nd 2011, 03:25 AMmetlx30 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 AMmetlxRe: 30 people, 365 days, birthday
Year doesn't matter. Just days in the year.

- Nov 22nd 2011, 06:34 AMSorobanRe: 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%

Sorry, your answer and your reasoning are wrong.

. . 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:

. . . . . $\displaystyle 1 - 92.4\% \;=\;7.6\%$