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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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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 = \(1-\frac{365!}{280!365^{85}}\)

ANswer is (d)
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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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