Interesting Birthday Problem
The answer is somehow counterintuitive:
I want to make a birthday party with 50% chance that at least two people will have the same birthday date, what is the minimal number of people I will have to invite? Supposing we do not count leap years and that I have to invite at least 2 people.
The answer is 23.
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1 solution
If we use complementary counting, the total chance of x number of people not sharing a birthday with anyone else out of the group is 365/365 * 364/365 * 363/365 * ... * (365-x)/365
When x hits 23, the probability is ~49% => the probability that at least two people will share a birthday is ~51%