GCSE Maths · Topic guide
Probability questions test whether you can turn a word problem into numbers between 0 and 1, and whether you know when to multiply (AND) or add (OR) — often via tree diagrams or sample spaces. ‘Without replacement’ changes the second draw; examiners love that trap. Show fractions on non-calculator papers unless told otherwise; give answers in simplest form.
Worked examples & mini quiz
P(A) = favourable outcomes / total equally likely outcomes. For independent events: P(A and B) = P(A) × P(B). For mutually exclusive: P(A or B) = P(A) + P(B). Use trees to structure multi-step problems.
Example 1
Single event
A bag has 3 red and 5 blue balls. P(red) = 3/8.
Example 2
Two independent events
P(coin heads) = 1/2, P(dice six) = 1/6. P(both) = 1/2 × 1/6 = 1/12.
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1. A fair die is rolled twice. P(both sixes) =
Correct: 1/36(1/6) × (1/6) = 1/36.
2. Events A and B are mutually exclusive if:
Correct: They cannot both happen in one trialMutually exclusive means no overlap; P(A or B) = P(A) + P(B).
3. On a probability tree, branch probabilities from the same node should:
Correct: Sum to 1All outcomes from that split are covered.
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