Probability, Sets, Venn Diagrams and Two-Way Tables

Starting point: Years 9 and 10

Basic probability

For equally likely outcomes:

$$P(\text{event})=\frac{\text{number of favourable outcomes}}{\text{total number of outcomes}}$$

Probabilities go from 0 (impossible) to 1 (certain). The list of all possible outcomes is the sample space.

The complement of an event is "it does not happen":

$$P(\text{not }A)=1-P(A)$$

Venn diagrams

So $P(\text{sport but not music})=\frac{13}{30}$ and $P(\text{neither})=\frac{5}{30}=\frac{1}{6}$.

Two-way tables

The same data can go in a table with totals.

Every row and column must add up to its total, which is a good way to check your work.

Quick summary

• $P(\text{event})=\frac{\text{favourable}}{\text{total}}$ and $P(\text{not }A)=1-P(A)$.
• In a Venn diagram, fill the overlap first. "And" is the overlap. "Or" is anything in either circle.
• Two-way tables show the same counts with row and column totals.
• $P(A\cup B)=P(A)+P(B)-P(A\cap B)$.
• $P(A\mid B)=\frac{P(A\cap B)}{P(B)}$. Independent if $P(A\cap B)=P(A)P(B)$.

Quiz