GCSE Maths · Topic guide
GCSE Maths probability revision
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.
Common mistakes in exams
- Using 'with replacement' probabilities when items aren't replaced.
- Adding probabilities that aren't mutually exclusive without adjusting overlap.
- Giving answers > 1 or negative.
- Rounding too early and breaking the sum-to-1 check on branches.
Worked examples & mini quiz
GCSE Maths: Probability basics
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.
Worked examples
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.
Mini quiz (3 questions)
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1. A fair die is rolled twice. P(both sixes) =
- A.1/36
- B.1/6
- C.1/12
- D.2/6
Show answer
Correct: 1/36
(1/6) × (1/6) = 1/36.
2. Events A and B are mutually exclusive if:
- A.They cannot both happen in one trial
- B.They always happen together
- C.P(A) = P(B)
- D.They are independent
Show answer
Correct: They cannot both happen in one trial
Mutually exclusive means no overlap; P(A or B) = P(A) + P(B).
3. On a probability tree, branch probabilities from the same node should:
- A.Sum to 1
- B.Multiply to 1
- C.Always be 1/2
- D.Be ignored
Show answer
Correct: Sum to 1
All outcomes from that split are covered.
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