This page gives you the key ideas to recognise before you start a question. The full course then takes you through the method, exam-style practice and fully worked solutions.
Define events clearly
Translate the wording into events before applying probability rules. This reduces errors in multi-stage questions.
Use complements
P(A′) = 1 − P(A) is often the quickest route when a question asks for “at least one” or the opposite of a named event.
Conditional probability
Conditional probability changes the sample space: you are working within the information after the condition is known.
Independence
Independent events do not affect each other. Do not assume independence unless it is stated or can be justified.
Worked example: a complement
If P(A) = 0.37:
P(A′) = 1 − P(A)
= 1 − 0.37
= 0.63
P(A′) = 1 − P(A)
= 1 − 0.37
= 0.63
Common mistakes to avoid
- Adding probabilities when events are not mutually exclusive.
- Multiplying probabilities without checking the structure of the events.
- Confusing mutually exclusive events with independent events.