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  1. #1
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    Question Help!

    There are 12 students. Compute the probability that at least 3 students are born in the same month.

    Am I right with:

    {12 \choose 3} \times (\frac{1}{12})^3

    OR

    (\frac{1}{3} \times \frac{1}{12}) + (\frac{1}{3} \times \frac{1}{12}) + (\frac{1}{3} \times \frac{1}{12})
    Last edited by zepher; April 19th 2008 at 09:01 AM.
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  2. #2
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    Quote Originally Posted by zepher View Post
    There are 12 students. Compute the probability that at least 3 students are born in the same month.

    Am I right with:

    {12 \choose 3} \times (\frac{1}{12})^3
    You have counted the probability of exactly 3 people born in the same month.
    A better way is to solve the problem the other way.

    Pr(at least 3 students are born in the same month) = 1 - Pr(exactly 2 people are born in the same month)
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  3. #3
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    Thanks!
    But actually, why does Pr(at least 3 students are born in the same month) = 1 - Pr(exactly 2 people are born in the same month) ?

    1 - Pr(exactly 2 people are born in the same month) can still have other cases besides having at least 3 students born in the same month right?

    Pls advise! ^_^
    Last edited by zepher; April 19th 2008 at 09:34 AM.
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  4. #4
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    Please look at the webpage: Birthday Problem -- from Wolfram MathWorld
    You will see that this is far from an easy problem.
    P.S. For this problem n=12 & d=12.
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  5. #5
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    I guess I should reduce the numbers a little.
    Say the question now is:
    There are 5 students. Compute the probability that AT LEAST 2 students are born in the same month.

    I will take:
    Pr(AT LEAST 2 students born in same month) = 1 - Pr(NONE of them born in same month)

    which is

    1 - (12_P_5 / 12^5)


    Please tell me I am correct =P
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