Find the probability of a single event as a fraction, decimal or percentage, and use the fact that probabilities sum to one

What this dot point is asking

SEAB wants you to measure how likely a single event is, expressing the probability as a fraction, decimal or percentage, and to use the fact that the probabilities of all outcomes add to $1$. Probability is about counting favourable outcomes against all possible outcomes, so careful counting is the main skill.

The answer

The probability scale

Probability measures how likely something is, on a scale from $0$ to $1$:

• A probability of $0$ means the event is impossible.
• A probability of $1$ means the event is certain.
• A probability of $\dfrac{1}{2}$ means it is as likely as not.

Probabilities can be written as fractions, decimals or percentages: $\dfrac{1}{2}$, $0.5$ and $50\%$ all describe the same chance.

Equally likely outcomes

When all outcomes are equally likely (a fair die, a well-shuffled pack), the probability of an event is:

For a fair die, the probability of rolling a $3$ is $\dfrac{1}{6}$, because one face out of six is favourable.

Counting outcomes carefully

The key step is counting correctly. List the favourable outcomes and the total outcomes, then form the fraction. For "an even number on a die", the favourable outcomes are $2, 4, 6$ (three of them), so the probability is $\dfrac{3}{6} = \dfrac{1}{2}$.

The complement rule

The outcomes of an event and its opposite (its complement) together cover everything, so their probabilities add to $1$:

If the probability of rain is $0.3$, the probability of no rain is $1 - 0.3 = 0.7$. This is often the quickest way to find a "not" probability.

Simplifying the answer

Give probabilities as simplified fractions unless told otherwise, for example $\dfrac{4}{8}$ written as $\dfrac{1}{2}$. A decimal or percentage is also acceptable when the question allows.

Examples in context

Example 1. A spinner. A spinner divided into $8$ equal sectors, $3$ of them red, gives a probability of red of $\dfrac{3}{8}$. Equal sectors make the outcomes equally likely, so the count of red sectors over the total sectors is the probability.

Example 2. Weather forecasts. When a forecast says there is a $70\%$ chance of rain, the chance of no rain is $100\% - 70\% = 30\%$. The complement rule turns one stated probability into its opposite instantly, which is how "not" probabilities usually arise in real life.

Try this

• Cue. A fair coin is tossed. The probability of heads is $\dfrac{1}{2}$, since one of two equally likely outcomes is favourable.
• Cue. A bag has $7$ white and $3$ black counters. The probability of black is $\dfrac{3}{10}$.
• Cue. If $\text{P(win)} = 0.4$, then $\text{P(not win)} = 1 - 0.4 = 0.6$.