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Math Help - probability

  1. #1
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    probability

    "Assume that the box contains 7 balls: 4 red, 2 green, and 1 yellow. Balls are drawn in succession without replacement, and their colors are noted until both a red and a green ball have been drawn."

    How many outcomes are there in the sample space?"


    the answer is 25, but i only know how to arrive at this answer by sketching a convoluted diagram or by racking my brain to figure out all the sets (RG, RRG, RRRG etc) and then counting the outcomes.

    is there a faster way to figure out the number of outcomes using algebra or some other method? i don't think i'll have enough time on the test to draw a diagram.


    thanks
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  2. #2
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    Quote Originally Posted by sdsdsd View Post
    "Assume that the box contains 7 balls: 4 red, 2 green, and 1 yellow. Balls are drawn in succession without replacement, and their colors are noted until both a red and a green ball have been drawn."

    How many outcomes are there in the sample space?"


    the answer is 25, but i only know how to arrive at this answer by sketching a convoluted diagram or by racking my brain to figure out all the sets (RG, RRG, RRRG etc) and then counting the outcomes.

    is there a faster way to figure out the number of outcomes using algebra or some other method? i don't think i'll have enough time on the test to draw a diagram.


    thanks
    I don't see too many short cuts here.
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  3. #3
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    Hello, sdsdsd!

    I agree with Mr. F . . . I see no "formula" approach.
    I think Brute Force listing is the only way . . .


    Two draws

    \begin{array}{c}RG \\ GR\end{array} . . . 2 ways.


    Three draws

    \begin{array}{c}RRG \\ RY\!G \\ Y\!RG \\ GGR \\ GY\!R \\ Y\!GR\end{array} . . . 6 ways


    Four draws

    \begin{array}{c}RRRG \\ RRY\!G \\ RY\!RG \\ Y\!RRG \\ GGY\!R \\ GY\!GR \\ Y\!GGR\end{array} . . . 7 ways


    Five draws

    \begin{array}{c}RRRRG \\ RRRY\!G \\ RRY\!RG \\ RY\!RRG \\ Y\!RRRG \end{array} . . . 5 ways


    Six draws

    \begin{array}{c}RRRRY\!G \\ RRRY\!RG \\ RRY\!RRG \\ RY\!RRRG \\ Y\!RRRRG \end{array} . . . 5 ways


    Total: 25 ways

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