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Math Help - Probability that of 3 people selected at random, at least 2 were born on the same day

  1. #1
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    Probability that of 3 people selected at random, at least 2 were born on the same day

    What is the probability that, of three people selected at random, at least two were
    born on the same day of the week?
    I know the answer is 19/49 but how?
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  2. #2
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    Quote Originally Posted by sundance240 View Post
    What is the probability that, of three people selected at random, at least two were
    born on the same day of the week?
    I know the answer is 19/49 but how?
    The back door method.
    (7/7)(6/7)(5/7) is the probability they were all born on different days of the week.
    Subtract that from 1. What do you get? WHY?
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  3. #3
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    Chance of at least two were born on the same day of the week = 1 - Chance of all three born on different days of the week

    Chance of three random people born on different days of the week = 1 * 6/7 * 5/7 = 30/49

    Chance of at least two were born on the same day of the week = 1 - 30/49 = 19/49

    Sorry for re-post, didn't see the above reply
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    I believe this is also called the birthday paradox. Birthday problem - Wikipedia, the free encyclopedia
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