This mini-lesson covers the Probability strand of AQA GCSE Maths (8300): the probability scale, sample space, tree diagrams, Venn diagrams, relative frequency, mutually exclusive & independent events, and conditional probability.
These games test recall of facts, formulae and methods — not full multi-step working. Answer the questions as you go and collect ⭐ stars. Press Start when you're ready.
All probabilities lie between 0 (impossible) and 1 (certain). They can be written as fractions, decimals or percentages.
Key rule: P(not A) = 1 − P(A). If the chance of rain is 0.3, the chance of no rain is 0.7.
When outcomes are equally likely:
A bag has 3 red and 5 blue counters. P(red)?
Favourable = 3, total = 3 + 5 = 8.
P(red) = 3/8
Total matters: the denominator is every outcome (3 + 5 = 8), not just the "other" colour.
Events are mutually exclusive if they can't both happen at once. For these, you add the probabilities:
A spinner: P(red) = 0.2, P(green) = 0.5. P(red or green)?
They can't both happen, so add: 0.2 + 0.5 = 0.7
Sum to 1: if red, green and blue are the only outcomes, P(blue) = 1 − 0.2 − 0.5 = 0.3.
Events are independent if one has no effect on the other. For these, you multiply the probabilities:
Two fair coins. P(heads and heads)?
Each P(head) = ½, and the coins are independent.
½ × ½ = ¼
AND × · OR +: multiply along the branches of a tree diagram (AND), then add the routes that give the outcome you want (OR).
A tree diagram shows all outcomes of two or more events. Multiply along each set of branches; the pairs at each fork sum to 1.
Two ways to get "one win": Win-Lose or Lose-Win. Work out each route, then add them.
When you can't count equally likely outcomes, estimate the probability from experiment:
A drawing pin lands "point up" 36 times out of 60 drops.
Relative frequency = 36 ÷ 60 = 0.6
Estimating a count: to predict results in N new trials, multiply the relative frequency by N.
Tap a fair-dice event on the left, then its probability on the right (a standard six-sided die).
Sort each phrase into the rule it needs. "OR" mutually exclusive events are added; "AND" independent events are multiplied. Tap a phrase, then the box.
Scale: 0 ≤ P ≤ 1; P(not A) = 1 − P(A); all outcomes sum to 1.
Single event: favourable ÷ total outcomes.
Mutually exclusive (OR): add — P(A or B) = P(A) + P(B).
Independent (AND): multiply — P(A and B) = P(A) × P(B).
Tree diagrams: multiply along branches, add the routes.
Relative frequency: times happened ÷ total trials.
Venn diagrams: overlap = in both; conditional probability narrows the sample space.
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