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Math Help - win-lose tree diagram possibilites

  1. #1
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    win-lose tree diagram possibilites

    1.draw a tree diagram to show the win-loss possibilities for one of the teams in a best two of three playoff series in Olympic volleyball

    after drawing it i get 27 possibilities, is this correct?
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  2. #2
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    Hello, William!

    How did you get 27?


    1. Draw a tree diagram to show the win-loss possibilities for one of the teams
    in a best two of three playoff series in Olympic volleyball.
    There are six possible series.


    \begin{array}{cccccccccc}<br />
& & & & & \ulcorner & \text{win} \\<br />
& & \;\;\ulcorner & \text{win} & - &\!\!\!\! \dashv & & & \ulcorner & \text{win} \\<br />
& & \;\;\vert & & & \llcorner & \text{lose} & - & \!\!\!\!\dashv  \\<br />
& & \;\;\vert &&&&&& \llcorner & \text{lose} \\<br />
* & - & \dashv\\<br />
& & \;\;\vert &&&&&& \ulcorner & \text{win} \\<br />
& & \;\;\vert & & &\; \ulcorner & \text{win} & - &\!\!\!\! \dashv \end{array}
    . . . . . \begin{array}{cccccccccc}<br />
& & \llcorner & \text{lose} & - & \!\!\!\!\dashv & & & \quad\llcorner &  \text{lose} \\<br />
& & & & & \llcorner & \text{lose}\end{array}

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  3. #3
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    Quote Originally Posted by Soroban View Post
    Hello, William!

    How did you get 27?


    There are six possible series.


    \begin{array}{cccccccccc}<br />
& & & & & \ulcorner & \text{win} \\<br />
& & \;\;\ulcorner & \text{win} & - &\!\!\!\! \dashv & & & \ulcorner & \text{win} \\<br />
& & \;\;\vert & & & \llcorner & \text{lose} & - & \!\!\!\!\dashv  \\<br />
& & \;\;\vert &&&&&& \llcorner & \text{lose} \\<br />
* & - & \dashv\\<br />
& & \;\;\vert &&&&&& \ulcorner & \text{win} \\<br />
& & \;\;\vert & & &\; \ulcorner & \text{win} & - &\!\!\!\! \dashv \end{array}
    . . . . . \begin{array}{cccccccccc}<br />
& & \llcorner & \text{lose} & - & \!\!\!\!\dashv & & & \quad\llcorner &  \text{lose} \\<br />
& & & & & \llcorner & \text{lose}\end{array}

    I misinterpreted the question thinking of win win lose, win win win, lose lose win, branching off of a team following the multiplication principle: 1*3*3*3=27
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