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Thread: Probability.......Average

  1. #1
    Trying to make mom and pop proud
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    Probability.......Average

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    3 positive integers are selected at random from 9 consecutive positive integers. What is the probability that their average is also an integer.

    a) 9/28

    b) 1/28

    c) 1/3

    d) 5/14

    e) 9/29

    SPOILER: D

  2. #2
    An Urch Guru Pundit Swami Sage chix475ntu's Avatar
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    Centrino .. where did you get this question.. seems to be HARDDDDDDDDDDDDDDDD BIN ...

    struggled for sometime but think this is the approach... i got the answer with this approach..

    the 9 numbers are
    3 are in the form 3n ( multiples of 3) ---- SET 1
    3 are in the form 3n+1 ---- SET 2
    3 are in the form 3n+2 ---- SET 3

    if you take the 3 numbers from the same set then the sum is divisible by 3 ..
    so we got 3 combinations here for 3 sets ..
    the only other way is taking 1 from each set ... so 3C1 * 3C1 * 3C1 = 27
    [ this is like 3n + 3n+1+3n+2 = 9n+3 which is divisible by 3]
    so total combinations = 3+27 = 30

    probability = 30/84 = 5/14

    D

  3. #3
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    Many thanks Chix.........I liked your logic.

  4. #4
    TestMagic Guru CTG1983's Avatar
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    It's probably the hardest probability problem. Is there any easier approach?

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