Possibility diagrams & dice

Probability tree & bag

Conditional probability diagrams

<p class="paragraph-header">Identify equally likely outcomes</p>
<p>When all elementary outcomes are equally likely, \(P(\text{event})=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}\). Count outcomes, not just the different values of a total.</p>
<p>For two distinguishable dice, an outcome records the first score and then the second. The pairs (1,2) and (2,1) are different outcomes even though they give the same total. A possibility table records each ordered outcome once.</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>Description</strong></th><th style="text-align: center; --cell-justify: center"><strong>Meaning</strong></th></tr></thead><tbody><tr><td style="text-align: center; --cell-justify: center">Exactly one success</td><td style="text-align: center; --cell-justify: center">One success and one failure in two trials</td></tr><tr><td style="text-align: center; --cell-justify: center">At least one success</td><td style="text-align: center; --cell-justify: center">One or more successes</td></tr><tr><td style="text-align: center; --cell-justify: center">At most one success</td><td style="text-align: center; --cell-justify: center">Zero or one success</td></tr></tbody></table></div></div>
<p>Mutually exclusive events cannot occur together. Independent events do not affect each other’s probability. These are different properties: two different faces on one die cannot occur together, while results on two independently rolled dice can.</p>
<p>Do not assume a device is fair or trials are independent unless this is stated or justified. A table of possible outcomes does not by itself make its cells equally likely.</p>

When all elementary outcomes are equally likely, \(P(\text{event})=\dfrac{\text{number of favourable outcomes}}{\text{total number of outcomes}}\). Count outcomes, not just the different values of a total.

For two distinguishable dice, an outcome records the first score and then the second. The pairs (1,2) and (2,1) are different outcomes even though they give the same total. A possibility table records each ordered outcome once.

Mutually exclusive events cannot occur together. Independent events do not affect each other’s probability. These are different properties: two different faces on one die cannot occur together, while results on two independently rolled dice can.

Do not assume a device is fair or trials are independent unless this is stated or justified. A table of possible outcomes does not by itself make its cells equally likely.

Outcomes and probability models

Outcomes and probability models

Description	Meaning
Exactly one success	One success and one failure in two trials
At least one success	One or more successes
At most one success	Zero or one success