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Math Help - Algebra 2 probability question

  1. #1
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    Algebra 2 probability question

    there are a bag of 7 marbles, 3 red 4 green

    if u pick 2 marbles, what is the probability of choosing one green and one red (order doesnt matter)?

    isn't it 3/7 x 4/6?

    i kno 4 nCr 1 x 3 nCr 1 divided by 7 nCr 2 is the correct answer but how is it different from 3/7 x 4/6?
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  2. #2
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    Hello, mairjuanaman!

    There are a bag of 7 marbles: 3 red, 4 green.

    if u pick 2 marbles, what is the probability of choosing one green and one red (order doesn't matter)?

    Isn't it 3/7 x 4/6 ? . . . . . no

    You found the probability of getting a Red, then a Green . . . in that order.

    P(\text{Red, then Green}) \:=\:\frac{3}{7}\times\frac{4}{6} \:=\:\frac{2}{7}

    And: . P(\text{Green, then Red}) \:=\:\frac{4}{7}\times\frac{3}{6} \:=\:\frac{2}{7}


    Therefore: . P(\text{Red and Green, either order}) \;=\;\frac{2}{7} + \frac{2}{7} \;=\;\frac{4}{7}


    This is the same answer as: . \frac{(_4C_1)(_3C_1)}{_7C_2}

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