How many people?
There are x people in a room, what is the smallest x such that there will be at least a 50 percent chance that two of these people will have the same birthday?
Just like to point out that 365 or 366 days in a year makes no difference in this problem if we assume that people are equally likely to be born on any day of the year. In reality, more people are born 9 months after New Years Eve or other holidays.
I think that if there was a direct approach, it would be very complicated and unwieldy to use. In this problem my first guess was 15; intuitively, you can rule out the chances that fewer than this number would be the right answer--especially very low numbers like 4 or 5. It would be esthetically pleasing, I must admit, to have a formula that takes you right to the answer without the need to make any guesses.
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