Trivia: The Birthday Paradox

In a room of 57 or more people, the probability of two people having the same birthday is 99%.

In a group of 23 randomly chosen people, that probability is 50%. For a full explanation, see Birthday Paradox [wiki]

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I takes a little while to get use to the idea... I am curious how to solve the Birthday Paradox without using this inversion approach.

Say there are 4 students in the class, what is the probability that 2 or more student has the same birthday? I would like to know how to so solve this WITHOUT using the inversion technique[1 - {364/365 * 363/365 * 362/365}]. I believe it involve some
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How is that a paradox or even surprising? The exact number needed to hit 99% might need a little math to figure out, but the fact it is around 57 should be no surprise to any high school graduate.

Your government schools at work.
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So with todays public education, math is now a strange and wonderful bit of magic to impress simpletons at gatherings.

How long until someone who can do simple math without a calculator is burned at the stake for witchcraft?
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Sad that this should become known as a paradox, as there is nothing paradoxical about it. It may be difficult to believe, but it does not contradict itself.
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