It is a famous probability problem called The Birthday Paradox.
It is used to compute that at least two people share the same birthday (ignore year) in some people in a room Or in a group of n people.
Now, I'm going to compute the probability in the following manner-
Probability of at least two people share the same birthday = $1- $ Probability of no people share the same birthday
Now, the first people can born in any day of the year (assuming it's a normal year not a leap year) = $\dfrac{365}{365}$
the second people can have $364$ possible birthdays, so the second people's probability is $\dfrac{364}{365}$
the third people can have $363$ possible birthdays, so the third people's probability is $\dfrac{363}{365}$
$\vdots $
$11^{th}$ number people can have $355$ (because $10^{th}$ number people have the possibility of $356$ birthdays) possible birthdays, & the probability will be $\dfrac{355}{365}$
∴ Probability of no two people have the same bday = $\dfrac{365}{365} \times \dfrac{364}{365} \times \dfrac{363}{365} \times \ldots \times \dfrac{355}{365}$
$\quad \quad \quad = \dfrac{365!}{(354! *(365^{11}))}$
∴ Probability of two people have same birthday $= 1-\dfrac{365!}{(354! *(365^{11}))} \\ = 0.1411 = 14.11\%$