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

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Re: If there are 85 students in a statistics class and we assume that ther [#permalink]
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Q51  V41
Re: If there are 85 students in a statistics class and we assume that ther [#permalink]
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Yalephd 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) $$\frac{85}{365} * \frac{84}{364}$$

B) $$\frac{1}{365} * \frac{1}{364}$$

C) 1 - $$\frac{85!}{365!}$$

D) 1 - $$\frac{365!}{280!(365^8^5)}$$

E) 1 - $$\frac{85!}{365^8^5)}$$

______________________________________________
This seems like a rather difficult question for the GMAT.

Probability(Atleast 2 share a bday) = 1 - Probability(All 85 have distinct birthdays)

total ways to pick 85 birthdays = 365^85
Ways to pick distinct 85 out of the 365 & distribute it to 85 people = C(365,85)*85!

Hence Probability = $$1-\frac{365!}{280!365^{85}}$$

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Re: If there are 85 students in a statistics class and we assume that ther [#permalink]
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Interestling enough, for 60 students, the answer already comes close to 99% . Interesting, huh?
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Re: If there are 85 students in a statistics class and we assume that ther [#permalink]
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Re: If there are 85 students in a statistics class and we assume that ther [#permalink]
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