The probability scale
The probability scale
- Probability measures how likely an event is, on a scale from $0$ (impossible) to $1$ (certain). $\tfrac12$ is an even chance.
- It can be a fraction, decimal or percentage. We write $\text{P}(A)$.
- For equally likely outcomes:
$$\text{P}(\text{event}) = \frac{\text{favourable outcomes}}{\text{total outcomes}}$$
Practice
What is the probability of an impossible event?
Impossible events have probability 0; certain events have probability 1.
Practice
Write the probability of an "even chance" as a decimal.
An even chance is ½ = 0.5.
The complement
- The probability an event does not happen:
$$\text{P}(A') = 1 - \text{P}(A)$$
- Worked example: a bag has $3$ red and $5$ blue. $\text{P}(\text{red}) = \tfrac38$, so $\text{P}(\text{not red}) = 1 - \tfrac38 = \tfrac58$.
Practice
A bag has 3 red and 5 blue counters. P(not red) = a/8. What is a?
P(red) = 3/8, so P(not red) = 1 − 3/8 = 5/8; a = 5.
You've got it
Key idea
- probability runs $0$ (impossible) to $1$ (certain); $\tfrac12$ is even chance
- $\text{P} = \dfrac{\text{favourable}}{\text{total}}$ for equally likely outcomes
- complement: $\text{P}(A') = 1 - \text{P}(A)$