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Math Help - 30 people, 365 days, birthday

  1. #1
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    30 people, 365 days, birthday

    There is 30 people in a group (29 + you).
    What's the probabillity that one of them has the exact same birthday as you?

    This is what I've got thus far. I have no idea how to check if it's correct though.

    30 * (1/365)^1 * (364/365)^29 = 0.076 = 7.6%
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  2. #2
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    Re: 30 people, 365 days, birthday

    Year doesn't matter. Just days in the year.
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  3. #3
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    Re: 30 people, 365 days, birthday

    Hello, metlx!

    There are 30 people in a group (29 + you).
    What's the probabillity that one of them has the exact same birthday as you?

    This is what I've got thus far.
    I have no idea how to check if it's correct though.

    30 * (1/365)^1 * (364/365)^29 = 0.076 = 7.6%

    Sorry, your answer and your reasoning are wrong.
    . . Your answer was:. 0.075905885 \:\approx\: 7.6\%
    But miraculously, you came out very close to the correct answer.


    If you want the probability that exactly one has your birthday,

    . . the probability is:. {29\choose1}\left(\frac{1}{365}\right)\left(\frac{  364}{365}\right)^{28} \:=\:0.07357727 \:\approx\:7.4\%


    If you want the probability that at least one has your birthday . . .

    The probability that no one has your birthday is:
    . . \left(\frac{364}{365}\right)^{29} \:=\:0.923521598 \:\approx\:92.4\%

    Therefore, the probability that at least one has your birthday is:
    . . . . . 1 - 92.4\% \;=\;7.6\%

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