What you'll learn
This topic covers basic probability — calculating probabilities, listing outcomes, and using sample space diagrams. In this guide you will learn the probability scale, how to find the probability of an event, how to list outcomes systematically, how to use sample space diagrams for two events, and the "probabilities sum to 1" rule. These are foundational data-handling skills.
Key terms and definitions
Probability — a measure of how likely an event is, from 0 to 1.
Outcome — a possible result of a trial.
Event — an outcome or set of outcomes you are interested in.
Sample space — the set of all possible outcomes.
Mutually exclusive — events that cannot happen at the same time.
Core concepts
The probability scale
Probability runs from 0 (impossible) to 1 (certain), written as a fraction, decimal or percentage. An even chance is ½. Words like "likely" and "unlikely" map onto this scale.
Calculating probability
For equally likely outcomes, P(event) = number of favourable outcomes ÷ total number of outcomes. For example, the probability of rolling a 3 on a fair die is 1/6, and of an even number 3/6 = ½.
Probabilities summing to 1
All the probabilities of an event either happening or not add up to 1, so P(not A) = 1 − P(A). For a set of mutually exclusive outcomes, their probabilities also sum to 1, which lets you find a missing probability.
Listing outcomes systematically
To avoid missing any, list outcomes systematically — in order, or in a table. For two events (e.g. two dice, or a coin and a spinner), a sample space diagram (a grid) shows every combination clearly.
Using sample space diagrams
A sample space diagram lists one event along the top and the other down the side, filling the grid with combined outcomes. Counting the favourable cells over the total cells gives the probability of a combined event.
Worked examples
Example 1: Single event
Find the probability of drawing a red card from a standard 52-card pack.
26 ÷ 52 = ½.
Example 2: Complement
P(rain) = 0.3. Find P(no rain).
1 − 0.3 = 0.7.
Example 3: Two dice
Using a sample space of two dice (36 outcomes), find P(total = 12).
Only 6 + 6, so 1 ÷ 36 = 1/36.
Common mistakes and how to avoid them
Probabilities outside 0 to 1. They must lie on the scale.
Forgetting the complement rule. P(not A) = 1 − P(A).
Missing outcomes. List systematically or use a grid.
Wrong total. Count all possible outcomes for the denominator.
Assuming unfair = equally likely. Only use the formula for equally likely outcomes.
Exam technique for Basic Probability
Place probabilities on the 0 to 1 scale.
Use favourable ÷ total for equally likely outcomes.
Apply P(not A) = 1 − P(A) and the sum-to-1 rule.
List outcomes systematically to avoid missing any.
Draw a sample space diagram for two combined events.
Quick revision summary
Probability runs from 0 (impossible) to 1 (certain) and can be a fraction, decimal or percentage. For equally likely outcomes, P(event) = favourable ÷ total (P(even on a die) = 3/6 = ½). All outcomes' probabilities sum to 1, so P(not A) = 1 − P(A), and for mutually exclusive events the probabilities also add to 1 — useful for finding a missing value. To count outcomes for two events, list them systematically or use a sample space diagram (a grid with one event on each axis), then count favourable cells over total cells. The common errors are giving probabilities outside 0 to 1, forgetting the complement rule, missing outcomes, and using the wrong total. Place probabilities on the scale, use favourable ÷ total, apply the sum-to-1 and complement rules, and draw sample space diagrams for combined events.