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Math Help - Simple Probability Question

  1. #1
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    Simple Probability Question

    Find the probability that in a group of 10
    people, all born in April, at least two have the same birthday.


    I thought of calculating the probability that no two people have the same birthday.

    April has 30 days, so

    1. person has 30/30 chance
    2. person has 29/30 chance
    3. person has 28/30 chance
    ...
    10. person has 21/30 chance
    to have a different birthday as the others.

    Then I get 29/30*28/30*...*21/30 = 0.185, which means there is a
    1 - 0.185 = 0.815 probability that 2 persons have the same birthday.

    I think thats too high, but thats all i can say.
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello EinStone
    Quote Originally Posted by EinStone View Post
    Find the probability that in a group of 10
    people, all born in April, at least two have the same birthday.


    I thought of calculating the probability that no two people have the same birthday.

    April has 30 days, so

    1. person has 30/30 chance
    2. person has 29/30 chance
    3. person has 28/30 chance
    ...
    10. person has 21/30 chance
    to have a different birthday as the others.

    Then I get 29/30*28/30*...*21/30 = 0.185, which means there is a
    1 - 0.185 = 0.815 probability that 2 persons have the same birthday.

    I think thats too high, but thats all i can say.
    No, your reasoning and answer are perfect!

    It does seem unlikely, but then so does this: Assuming all months are the same length and that birthdays are randomly distributed throughout the year, did you know that the odds that, in a group of 5 people, at least two will have birthdays in the same month are nearly 2:1 in favour? (In fact, it's 89:55.) Use the same method to work it out. Surprising, isn't it?

    Grandad
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