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If there are 85 students in a statistics class and we assume

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Joined: 25 Aug 2007
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If there are 85 students in a statistics class and we assume [#permalink]

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05 Jun 2010, 07:53
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If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)?

A. 85/365 * 84/365
B. 1/365 * 1/365
C. 1 - 85!/365!
D. 1 - 365!/(280!*365^85)[/m])
E. 1 - 85!/365^85
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Last edited by Bunuel on 31 Mar 2012, 02:04, edited 2 times in total.
Edited the question and added the OA

Kudos [?]: 1465 [0], given: 40

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Joined: 02 Sep 2009
Posts: 41698

Kudos [?]: 124658 [2], given: 12079

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05 Jun 2010, 07:59
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ykaiim wrote:
If there are 85 students in a statistics class and we assume that there are 365 days in a year, what is the probability that at least two students in the class have the same birthday (assuming birthdays are distributed independently)?

A) 85/365 x 84/365
B) 1/365 x 1/365
C) 1 - 85!/365!
D) 1 - 365!/(280! x $$365^8^5$$)
E) 1 - 85!/$$365^8^5$$

This question was posted in PS forum, below is my solution from there:

The easiest way to solve this problem is to calculate opposite probability and subtract this value from 1:

The opposite probability is that all students have the birthdays on different days: $$\frac{365}{365}*\frac{364}{365}*\frac{363}{365}*...*\frac{281}{365}=\frac{365*364*363*...*281}{365^{85}}=\frac{365!}{280!*365^{85}}$$ total 85 birthdays (first student can have birthday on any day =1=365/365, the probability that the second student will have the birthday on another day is 364/365, the probability that the third student will have the birthday not on this two days is 363/365, and so on).

So, the probability that at least two students in the class have the same birthday is: $$1-\frac{365!}{280!*365^{85}}$$.

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Kudos [?]: 124658 [2], given: 12079

Re: Same birthday probability   [#permalink] 05 Jun 2010, 07:59
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If there are 85 students in a statistics class and we assume

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