Probability · KS3 Maths

The probability scale

Probability measures how likely something is, from 0 (impossible) to 1 (certain). An even chance is 0.5.
Probabilities can be written as fractions, decimals or percentages.
If the outcomes are equally likely: probability = number of ways it can happen ÷ total number of outcomes. The probability of rolling a 6 on a fair dice is 1/6.

The probabilities of all the possible outcomes add up to 1.
The probability of something not happening = 1 − the probability that it happens. If P(rain) = 0.3, then P(no rain) = 0.7.

List all the outcomes systematically. Two coins: HH, HT, TH, TT (4 outcomes). Two dice: a sample space diagram with 6 × 6 = 36 outcomes.
The probability of two heads is 1/4. The probability of a total of 7 with two dice is 6/36 = 1/6.

Expected frequency = probability × number of trials. Roll a dice 60 times and you would expect about 60 × 1/6 = 10 sixes.
Relative frequency (experimental probability) = number of times it happens ÷ number of trials. More trials give a better estimate.

Probability: How likely something is to happen, from 0 to 1.
Outcome: A 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.
Fair: Every outcome is equally likely.
Sample space: A list or table of all the possible outcomes.
Expected frequency: How many times you expect something to happen: probability × number of trials.
Relative frequency: How often something happened in an experiment ÷ the number of trials.