# Math Help - Likelihood

1. ## Likelihood

Hi!

If there are 10 people in the same room and they were all born in the same year what would be the likelihood that at least two of them were born exactly the same day?

2. Originally Posted by Shandy
Hi!

If there are 10 people in the same room and they were all born in the same year what would be the likelihood that at least two of them were born exactly the same day?

The probability is 1 - the probability of them all being born on different days.

$p = 1 - \frac{365!}{365^{10}(365-10)!}$

$p = 1 - \frac{365\times 364\times 363\times 363 \ldots 356}{365^{10}}$

$p \approx 0.1169481777$

3. Originally Posted by Shandy
Hi!

If there are 10 people in the same room and they were all born in the same year what would be the likelihood that at least two of them were born exactly the same day?