The probability scale
- Probability measures how likely something is, from 0 (impossible) to 1 (certain). It can be written as a fraction, a decimal or a percentage.
- Words for likelihood: impossible, unlikely, even chance (½), likely, certain.
Equally likely outcomes
- P(event) = number of ways it can happen ÷ total number of equally likely outcomes.
- Rolling a fair dice: P(even) = 3/6 = ½. Picking from 3 red and 5 blue counters: P(red) = 3/8.
When something does not happen
- P(not A) = 1 − P(A). If P(rain) = 0.3, then P(no rain) = 0.7.
- The probabilities of all the possible outcomes add up to 1. If P(red) = 0.2 and P(blue) = 0.5, and green is the only other colour, then P(green) = 0.3.
Sample spaces
- A sample space lists every possible outcome. Rolling two dice gives 6 × 6 = 36 outcomes, and 6 of them total 7, so P(total of 7) = 6/36 = 1/6.
- List outcomes in a system so you don't miss any.
- Mutually exclusive events cannot happen at the same time. For them, P(A or B) = P(A) + P(B).
Key terms
- Probability
- How likely something is to happen, from 0 to 1.
- Outcome
- One possible result, such as rolling a 4.
- Event
- One or more outcomes, such as rolling an even number.
- Equally likely
- Having the same chance of happening.
- Sample space
- A list or table of all the possible outcomes.
- Mutually exclusive
- Events that cannot happen at the same time.
- Fair
- Having equally likely outcomes; not biased.