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Thread: A probability question

  1. #1
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    A probability question

    A pool (infinite) of coloured marbles 7 colours in total with equal proportion. 4 marbles are chosen, what is the probability that at least 2 of the same colour.

    I did 1-P(all different) which is 1-7/7*6/7*5/7*4/7

    Also tried the "direct" approach

    2 same: 1/7*1/7*6/7*5/7*4C2*7 where the 4C2 is to choose which 2 to be the same and 7 is to account for 7 colours

    3 same: 1/7*1/7*1/7*6/7*4C3*7

    4 same: 1/7*1/7*1/7*1/7*7

    But when I add up it does not tally with my first approach.

    What went wrong? Appreciate if anyone can help.

    Thanks.
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  2. #2
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    Re: A probability question

    Quote Originally Posted by acc100jt View Post
    A pool (infinite) of coloured marbles 7 colours in total with equal proportion. 4 marbles are chosen, what is the probability that at least 2 of the same colour.
    I did 1-P(all different) .
    You have absolutely the correct approach. But this is a multi-selection question.
    The number of ways to select $N$ items from $K$ different possibilities is $\binom{N+K-1}{N}$
    So $\binom{4+7-1}{4}=210$ See Here.

    How many of those are all of the same colours?
    Last edited by Plato; Jul 8th 2017 at 05:36 PM.
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