There are 32 students in a class-room. What is the probability that at least 3 of them have their birthdays in the same month? How to get the total possibilities?
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Hint: 2*12 = 24. – Gamma Function Jun 17 '13 at 05:58
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Didnot get it? why 2*12 ? – mathphy Jun 17 '13 at 06:14
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Do you mean month or date? 25 would be a sufficient number in the standard Gregorian calendar, however in the Bahá'í calendar there are 18 months and then this is a legitimate probability problem. – AD - Stop Putin - Jun 17 '13 at 06:37
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Same months mean in ay date of that month. So if we cross 24, then the probability will still 1? Can anyone show me this details mathematically? – mathphy Jun 17 '13 at 06:40
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The probability is $1$ by the pigeon-hole principle. If order to have at most two students per month, there cannot be more than 24 students.
Hagen von Eitzen
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@mathphy On the contrary, it is impossible to avoid having at least three in the same month (that' what probability $1$ says) – Hagen von Eitzen Jun 17 '13 at 06:13
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I wanted to get it by the law, $P =\frac{possible* outcome}{total*possibilities}$ – mathphy Jun 17 '13 at 06:18
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@mathphy Of course the probabiliy cannot exced one. For a discussion how to compute such a probability when a computation is necessary in the first place, see http://math.stackexchange.com/questions/5005/birthday-probability – Hagen von Eitzen Jun 17 '13 at 06:25