The probability scale
- Probability measures how likely an event is, from 0 (impossible) to 1 (certain). Write it as a fraction, decimal or percentage.
- For equally likely outcomes, P(event) = number of ways it can happen ÷ total number of outcomes. P(even number on a fair dice) = 3 ÷ 6 = 1/2.
- The probabilities of all possible outcomes add up to 1, so P(not A) = 1 − P(A). If P(rain) = 0.35, P(no rain) = 0.65.
Experimental probability
- Relative frequency (experimental probability) = number of times the event happens ÷ number of trials. 18 heads in 50 throws gives 0.36.
- The more trials, the more reliable the estimate. Relative frequency is used when outcomes aren't equally likely, such as a biased dice.
- Expected frequency = probability × number of trials. If P = 0.2 and there are 150 trials, expect 30.
Sample spaces
- A sample space diagram lists every possible outcome. Two dice give 36 outcomes. 6 of them sum to 7, so P(sum of 7) = 6/36 = 1/6.
Risk
- Risk is the probability of something harmful. Absolute risk = number affected ÷ total, such as 4 in 100.
- Relative risk compares two groups: risk in one group ÷ risk in the other. 4 in 100 compared with 2 in 100 gives a relative risk of 2, so the risk is twice as high.
Key terms
- Probability
- How likely an event is, from 0 to 1.
- Relative frequency
- The number of times an event happens divided by the number of trials.
- Expected frequency
- Probability multiplied by the number of trials.
- Sample space
- A list of all possible outcomes.
- Biased
- Not fair, so outcomes aren't equally likely.
- Absolute risk
- The probability of a harmful event in a group.
- Relative risk
- The risk in one group divided by the risk in another.