Chance

Some actions have a result we cannot predict — flipping a coin, rolling a die, or playing a game. We call such an action a random experiment: it can be repeated under the same conditions, all its possible results are known in advance, but nobody can tell with certainty which one will happen. Probability is a mathematical way to measure how likely an event of the experiment is, such as “rolling a 6” when a die is rolled.

We use special words to describe the chance of an event happening. We can place these words on a line from least likely to most likely.

When you flip a fair coin, there are two possible outcomes: heads or tails. The chance of getting heads is 1 out of 2. We can write this as a fraction:

A probability can be found by counting when all the outcomes have the same chance — we say they are equally likely: a fair die, a fair coin, a fair spinner cut into equal parts. When exactly one of the \(n\) equally likely outcomes makes the event happen, there is one chance in \(n\): \(P(\text{event}) = \frac{1}{n}\). With a fair die, \(P(\text{rolling a } 5) = \frac{1}{6}\).
When the outcomes are equally likely and several of them make the event happen, we count them: $$P(\text{event}) = \frac{\text{number of outcomes that make the event happen}}{\text{number of outcomes}}$$ Both spinners below spin fairly: the pointer has the same chance of stopping in two parts of the circle of the same size. Spinner A has \(6\) equal parts and \(2\) of them are red: \(P(\text{red}) = \frac{2}{6}\), two chances in six.
When the outcomes do not have the same chance, we cannot count this way. Spinner B has three colours, but \(P(\text{red})\) is not \(\frac{1}{3}\): red covers half of the spinner, so on each spin red is more likely than blue or green, and \(P(\text{red}) = \frac{1}{2}\).