This mini-lesson covers Probability for Cambridge IGCSE Mathematics (0580): the probability scale, relative frequency, possibility diagrams, tree diagrams, Venn diagrams and combined events (Extended content included).
Honest heads-up: these games test recall of the rules and results, not full working. Show fractions and diagrams in the exam.
Answer as you go and collect ⭐ stars. Press Start.
The probability scale
The probability scale
Probability runs from 0 (impossible) to 1 (certain). For equally likely outcomes:
P(event) = favourable outcomes ÷ total outcomesP(not A) = 1 − P(A)
Worked example
A fair die: P(rolling a 5) = 1/6. P(not a 5) = 1 − 1/6 = 5/6.
Calculate
Your turn
1A bag has 3 red and 7 blue counters. Work out P(red) as a decimal.
Hint: 3 red out of 10 total = 3/10 = 0.3.
Calculate
Your turn
2The probability it rains tomorrow is 0.35. Work out the probability it does not rain.
Hint: P(not rain) = 1 − 0.35.
Relative frequency
Relative frequency
Relative frequency (experimental probability) estimates probability from data:
relative frequency = number of successes ÷ number of trialsmore trials → closer to the true probability
Worked example
A drawing pin lands "point up" 30 times in 50 throws: relative frequency = 30/50 = 0.6.
Calculate
Your turn
3A spinner is spun 200 times and lands on green 50 times. Work out the relative frequency of green as a decimal.
Hint: 50 ÷ 200.
Combined events & trees
Combined events & tree diagrams
For independent events use the rules:
AND → multiply · OR (mutually exclusive) → addtree diagram branches multiply along, add between
Worked example
Two fair coins: P(two heads) = ½ × ½ = ¼.
Watch dependency: "without replacement" changes the second probability — the total drops by one.
Calculate
Your turn
4A fair coin is tossed twice. Work out P(heads then heads) as a decimal.
Hint: ½ × ½ = 0.5 × 0.5.
Calculate
Your turn
5P(A) = 0.4 and P(B) = 0.5, and A and B are independent. Work out P(A and B).
Hint: multiply for independent AND: 0.4 × 0.5.
Quick check
Quick check
?Two events are independent. Which rule gives P(both happen)?
Venn & possibility diagrams
Venn & possibility diagrams
A Venn diagram shows overlap: the intersection A ∩ B is the middle; the union A ∪ B is everything in either circle. A possibility diagram lists every outcome of two events in a grid.
Worked example
Two dice: a 6×6 grid has 36 equally likely outcomes. P(total = 7) = 6/36 = 1/6.
Union rule: P(A ∪ B) = P(A) + P(B) − P(A ∩ B) — subtract the overlap so it isn't double-counted.
Calculate
Your turn
6Two fair dice are rolled. Using a 6×6 possibility grid (36 outcomes), how many outcomes give a total of 7?
Hint: (1,6),(2,5),(3,4),(4,3),(5,2),(6,1).
Quick check
Quick check
?Two fair dice are rolled. What is P(total = 7)?
Match game
Event ⇄ probability
Tap an event (fair die or coin), then its probability.
Sort it
Certain range?
Sort each value: could it be a valid probability (between 0 and 1) or not? Tap it, then its box.
✓ Valid (0 to 1)
✗ Impossible value
Recap
Key points
Scale: 0 to 1; P(not A) = 1 − P(A).
Relative frequency: successes ÷ trials.
Combined: AND → ×, OR (exclusive) → +.
Trees: multiply along branches, add between outcomes.
Venn: P(A ∪ B) = P(A) + P(B) − P(A ∩ B).
You've covered the Probability essentials for Cambridge IGCSE Maths (0580). Press Finish to see your score.
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