Probability tree & bag

Possibility diagrams & dice

Conditional probability diagrams

<p class="paragraph-header">Multiply along a path</p>
<p>For independent trials, the probability used at a later stage is unchanged by earlier results. Multiply the probabilities along a complete path to find the probability of that sequence.</p>
<p class="paragraph-header">Add disjoint alternatives</p>
<p>If&nbsp;\(W\) means a win and \(N\) means not a win, exactly one win in two games is \(WN\) or \(NW\). These two sequences cannot both occur, so add their probabilities.</p>
<div class="content-block content-block--table"><div class="table-container"><table style="width: 100%;"><thead><tr><th style="text-align: center; --cell-justify: center"><strong>Event in two games</strong></th><th style="text-align: center; --cell-justify: center"><strong>Sequences</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Both wins</td><td style="text-align: center; --cell-justify: center">WW</td></tr><tr><td style="text-align: center; --cell-justify: center">Exactly one win</td><td style="text-align: center; --cell-justify: center">WN or NW</td></tr><tr><td style="text-align: center; --cell-justify: center">At least one win</td><td style="text-align: center; --cell-justify: center">WW, WN or NW</td></tr><tr><td style="text-align: center; --cell-justify: center">No wins</td><td style="text-align: center; --cell-justify: center">NN</td></tr></tbody></table></div></div>
<p>An event and its complement include all outcomes without overlap: \(P(A^{\prime})=1-P(A)\). In particular, \(P(\text{at least one success})=1-P(\text{no successes})\).</p>
<p>“Not a win” may include a draw as well as a loss. Use a label whose meaning matches the information supplied. Do not assume independence merely because attempts occur at different times.</p>

For independent trials, the probability used at a later stage is unchanged by earlier results. Multiply the probabilities along a complete path to find the probability of that sequence.

If \(W\) means a win and \(N\) means not a win, exactly one win in two games is \(WN\) or \(NW\). These two sequences cannot both occur, so add their probabilities.

An event and its complement include all outcomes without overlap: \(P(A^{\prime})=1-P(A)\). In particular, \(P(\text{at least one success})=1-P(\text{no successes})\).

“Not a win” may include a draw as well as a loss. Use a label whose meaning matches the information supplied. Do not assume independence merely because attempts occur at different times.

Independent paths and complements

Independent paths and complements

Event in two games	Sequences
Both wins	WW
Exactly one win	WN or NW
At least one win	WW, WN or NW
No wins	NN