This mini-lesson covers the Probability strand of Eduqas GCSE Maths: the probability scale, sample space, P(not A), mutually exclusive and independent events, tree diagrams, Venn diagrams and relative frequency (experimental probability).
Work through each screen, answer the questions as you go (most are calculations) and collect ⭐ stars. Press Start when you're ready.
Every probability is a number from 0 to 1. For equally likely outcomes:
The probabilities of all possible outcomes add to 1. So the chance an event does not happen is:
A fair spinner has 8 equal sections, 3 shaded red. Find P(not red).
P(red) = 3 ÷ 8 = 0.375
P(not red) = 1 − 0.375 = 0.625
Common slip: probabilities are never bigger than 1 and never negative. An answer like 1.4 or −0.2 means a mistake.
A sample space lists every possible outcome. Once you can see them all, probabilities are just counting. Here is the sample space for rolling two fair dice and adding the scores:
Watch out: with two dice there are 36 outcomes, not 12 or 11. Totals from 2 to 12 are not equally likely — count them from the grid.
For a single pick, count the favourable items over the total items. A bag holds 3 red and 2 blue counters (5 in total):
A bag has 4 green and 6 yellow sweets. Find P(green).
Total = 4 + 6 = 10
P(green) = 4 ÷ 10 = 0.4
Always find the total first. The denominator is every item in the bag, not just the ones you don't want.
Two events are mutually exclusive if they cannot both happen at the same time (like rolling a 3 and rolling a 5 on one die). For mutually exclusive events you add the probabilities:
A spinner: P(red) = 0.2, P(green) = 0.5. Find P(red or green).
They can't both come up, so add:
0.2 + 0.5 = 0.7
Careful: only add when events can't overlap. "King" and "Heart" from a deck are not mutually exclusive — the King of Hearts is both — so you can't simply add those.
Two events are independent if one has no effect on the other (like two separate coin flips). For independent events you multiply:
A tree diagram shows the branches. Multiply along the branches for "and", then add across the ends for "or". Here two counters are drawn with replacement from the 3-red, 2-blue bag (P(red) = 0.6, P(blue) = 0.4):
Multiply, don't add: for "A and B" you multiply along branches. Adding 0.6 + 0.6 = 1.2 is impossible for a probability — a clear warning sign.
Tap an event on the left, then its matching probability on the right.
Note: these games test recall of facts, formulae and methods — not full written working. In the exam you must always show your working.
A Venn diagram sorts things into sets. The overlap is the items in both sets; add up the region you need, then divide by the total. Here 30 students said whether they study French (F) or Spanish (S):
Don't double-count the middle: the 7 in the overlap study both. "French only" is 11, but "studies French" includes the overlap too, so it's 11 + 7 = 18.
When outcomes are not equally likely (a biased die, a drawing pin), you estimate probability from an experiment:
A drawing pin lands "point up" 45 times in 60 drops. Estimate P(point up).
relative frequency = 45 ÷ 60 = 0.75
Estimated frequency: to predict how many times an event happens in N trials, multiply: expected = P × N. E.g. 0.75 × 200 = 150 times.
Two events are mutually exclusive if they cannot both happen at once. Tap a pair of events, then tap the box it belongs in.
Scale: probabilities run 0 (impossible) to 1 (certain); P(A) = favourable ÷ total.
P(not A): = 1 − P(A); all outcomes add to 1.
Sample space: list every outcome, then count (two dice → 36 outcomes).
Mutually exclusive: can't both happen → P(A or B) = P(A) + P(B).
Independent: no effect on each other → P(A and B) = P(A) × P(B).
Tree diagrams: multiply along branches, add across ends.
Venn diagrams: the overlap = both sets; don't double-count the middle.
Relative frequency: = frequency ÷ trials — experimental estimate of probability.
You've covered every sub-topic in the Eduqas GCSE Maths Probability strand. Press Finish to see your score.
You've worked through the Probability strand for Eduqas GCSE Maths. 🎉
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Next: test yourself in the Evaluate stage Confidence Quiz, then lock it in with Verify.