Probability Formulas – IGCSE Maths
Every probability formula you need for Cambridge IGCSE Mathematics 0580, with clear explanations of when to use each rule and how to set out your working.
Probability of an event
CoreThe basic probability formula for an equally-likely sample space.
When to Use
Use when every outcome is equally likely (fair dice, fair coin, single ball drawn at random).
Always check that outcomes are equally likely before applying this formula.
Complement rule
CoreThe probability that an event does not occur.
When to Use
Use when it is easier to find the probability of the event NOT happening.
Common shortcut for 'at least one' problems — find P(none) first, then subtract from 1.
Addition rule (mutually exclusive)
CoreFor events that cannot both happen at the same time.
When to Use
Use only when events cannot overlap, e.g. rolling a 3 OR a 5 on a single die.
Check that events truly are mutually exclusive before adding probabilities.
Multiplication rule (independent)
CoreFor events whose outcomes do not affect each other.
When to Use
Use for two coin flips, two dice, or 'with replacement' selection.
Multiply along branches of a tree diagram to get the probability of a path.
Relative frequency
CoreAn estimate of probability from observed data.
When to Use
Use when probability is not given, e.g. estimating from experimental results.
More trials gives a more reliable estimate of theoretical probability.
Expected frequency
CoreThe expected number of times an event occurs in n trials.
When to Use
Use to predict outcomes over many trials, e.g. expected number of sixes in 60 rolls.
Round sensibly — expected frequency must match the context (whole people, whole days).
Conditional probability
ExtendedThe probability of B given that A has happened.
When to Use
Use for 'without replacement' problems and given-information questions.
On a tree diagram, the second-branch probabilities are conditional probabilities.
Multiplication rule (dependent)
ExtendedFor dependent events where the second event’s probability depends on the first.
When to Use
Use for 'without replacement' problems — the denominator changes after the first selection.
Decrease both numerator and denominator if the same colour/object is taken without replacement.
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Book a Free TrialFrequently Asked Questions
Which probability formulas are given in the IGCSE 0580 exam?
None of the probability formulas are given in the formula sheet — you must memorise them. Focus on the addition rule, multiplication rule, complement rule, and conditional probability for Extended.
Do I multiply or add probabilities on a tree diagram?
Multiply along the branches to find the probability of a single path, then add the probabilities of different paths that satisfy the question.
What is the difference between independent and mutually exclusive events?
Independent events do not affect each other (e.g. two coin tosses). Mutually exclusive events cannot happen at the same time (e.g. rolling a 3 OR a 5). Independent events use multiplication; mutually exclusive events use addition.
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