Question

Assume that there are 56 students in this class. what is the probability that at least two students share a? birthday

Answer 1

P(at least 2 students have the same birthday)= 1- P(no 2 students have the same birthday)

Because P(A)=1-P(A'), where A is an event, and A' the complement of that event.

P(no 2 students have the same birthday)=

$\frac{365}{365}* \frac{364}{365}*\frac{363}{365}*\frac{362}{365}*... \frac{310}{365}$

think of the problem as follows. We have an urn of balls, numbered from 1 to 365 (the number of the days of the year. 

What is the probability of picking 56 different numbered balls, with replacements?

The first one can be any of the 365

the second any of 364 (since one selection has already been made)

the third any of the 363
.
.
and so on

the 56th selection is one of 310 left


Answer: 

$\frac{365}{365}* \frac{364}{365}*\frac{363}{365}*\frac{362}{365}*... \frac{310}{365}$