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Math Help - Did I do this correctly?

  1. #1
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    Did I do this correctly?

    There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

    100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

    is equal to (by the binomial theorem)

    100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

    = .546%
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  2. #2
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    Quote Originally Posted by jmedsy View Post
    There are 40 students in our combinatorics class. Use combinatorial principles to compute the probability that at least two people in class have the same birthday (assume 365 days in a year)...

    100% * summation from i=2 to 40 of ((40 choose i) * (1/365)^i * (364/365)^(40-i))

    is equal to (by the binomial theorem)

    100% * ((1/365 + 364/365)^40 - (40 choose 0) * (1/365)^0 * (364/365)^40 - (40 choose 1) * (1/365) * (364/365)^39)

    = .546%
    Check your answer here: Birthday problem - Wikipedia, the free encyclopedia
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  3. #3
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    Am I right to say my calculation yields the odds of at least 2 people in a class of 40 having a birthday on one particular day of the year rather than having the same inexplicit birthday?

    Regardless, that link was helpful, thank you.
    Last edited by jmedsy; January 30th 2010 at 09:25 PM.
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