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Edexcel GCSE Maths

Probability: trees, Venn diagrams and conditional probability — Edexcel GCSE Maths revision

Free revision notes, key terms, common exam traps and 5 practice questions with answers. About 7 minutes to read.

Basic probability rules

  • P(event) = favourable outcomes ÷ total outcomes, always between 0 and 1.
  • P(not A) = 1 − P(A). Probabilities of all outcomes in a sample space sum to 1.
  • For mutually exclusive events, P(A or B) = P(A) + P(B).

Tree diagrams

  • Multiply along branches to find the probability of a combined outcome.
  • Add the results of separate branches when there is more than one route to the outcome.
  • Without replacement, the second set of branches changes because the total reduces.

Key terms

Sample space
The set of all possible outcomes of an experiment.
Mutually exclusive
Events that cannot happen at the same time.
Independent events
Events where one happening does not affect the probability of the other.
Intersection (∩)
Outcomes belonging to both sets.
Union (∪)
Outcomes belonging to either set (or both).
Conditional probability
The probability of an event given that another event has occurred.

Common exam traps

  • Forgetting to change denominators for 'without replacement' problems.
  • Adding probabilities along a tree branch instead of multiplying.
  • Multiplying instead of adding when there are two different routes to the same outcome.

Practice questions with answers

  1. 1. A bag has 4 red and 6 blue balls. Find P(red).

    Answer: 2/5

    4 red out of 10 total = 4/10 = 2/5.

  2. 2. P(rain) = 0.3. Find P(no rain).

    • • 0.3
    • • 0.7
    • • 1.3
    • • 0

    Answer: 0.7

    1 − 0.3 = 0.7.

  3. 3. A coin is flipped twice. Find P(two heads).

    Answer: 1/4

    1/2 × 1/2 = 1/4.

  4. 4. A bag has 5 red, 3 blue counters. One is drawn, not replaced, then another drawn. Find P(both red).

    Answer: 5/14

    5/8 × 4/7 = 20/56 = 5/14.

  5. 5. Events A and B are mutually exclusive with P(A)=0.2, P(B)=0.5. Find P(A or B).

    • • 0.1
    • • 0.7
    • • 0.3
    • • 1.0

    Answer: 0.7

    Mutually exclusive: add probabilities, 0.2+0.5=0.7.

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