win-lose tree diagram possibilites

**william** · February 8th 2009, 08:49 AM

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?

**Soroban** · February 8th 2009, 10:01 AM

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.

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

**william** · February 8th 2009, 10:08 AM

Originally Posted by Soroban

Hello, William!

How did you get 27?

There are six possible series.

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

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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