Probability measures how likely an event is. It is always a number from 0 (impossible) to 1 (certain), and can be written as a fraction, decimal or percentage.
Equally likely outcomes
When all outcomes are equally likely, use the simple formula below.
Key idea
P(event) = number of favourable outcomes / total number of outcomes.
The complement
The probability that an event does not happen is 1 minus the probability that it does. This is useful because it is often easier to work out the chance of an event not occurring. The set of all possible outcomes is called the sample space, and the probabilities of all the separate outcomes always add up to 1.
Key idea
P(not A) = 1 − P(A).
Relative frequency
When outcomes are not equally likely, or an experiment is repeated many times, we estimate probability using relative frequency = number of successes / number of trials. The more trials you carry out, the closer this estimate usually gets to the true probability.
Worked example
A bag holds 3 red and 5 blue counters, 8 in total. One counter is taken at random.
P(red) = 3/8.
P(not red) = 1 − 3/8 = 5/8, which matches the 5 blue counters out of 8. As a decimal this is 0.625, or 62.5%.
Probabilities can be written as fractions, decimals or percentages, and you should be comfortable changing between them. A value near 0 means the event is unlikely, a value near 1 means it is very likely, and a value of 0.5 means it is as likely to happen as not. Always simplify a fraction to its lowest terms in your final answer.
Remember
- All probabilities lie between 0 and 1.
- P(impossible) = 0; P(certain) = 1.
- Always simplify fractions where possible.