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The Birthday Problem

How large must a class be to make the probability
of finding two people with the same birthday at least 50%?

In a group of at least 23 randomly chosen people,
there is more than 50% probability that some pair
of them will both have been born on the same day.
For 57 or more people, the probability is more than 99%,
and it reaches 100% when the number of people reaches 366.

The Probability of having two people with the same birthday
in a group of n people can be calculated using -

P(same birthday) = 1 - 364/365 x 363/365 x 362/365 x ...
repeat to (n-1) times.

For 4 people P(same birthday) = 1.6%
For 10 people P(same birthday) = 11.7%
For 23 people P(same birthday) = 50.7%
For 57 people P(same birthday) = 99.0%
For 365 people P(same birthday) = 100.0%
For 500 people P(same birthday) = 100.0%