GCSE Mathematics
GCSE Maths: Probability Revision
Probability revision for GCSE and iGCSE Maths
Probability is a topic where a small number of ideas cover a large share of the marks. Almost every question comes down to counting the outcomes correctly, and then deciding whether events combine by adding or by multiplying. This free revision engine covers the probability content of GCSE and International GCSE Maths, from listing outcomes through to conditional probability without replacement. It generates a new question every time and marks your answer as you go.
What the probability revision engine covers
Foundation and Higher Basic probability — single events, and the probability of an event not happening Mutually exclusive events — probabilities that add to 1 Relative frequency — estimating a probability from experimental data Sample space diagrams — two dice, two coins, and compound conditions Expected frequency — how many times an event should happen over n trials Venn diagrams — reading probabilities from overlapping sets Two-way tables — reading and completing them The AND and OR rules — for independent and mutually exclusive events Higher tier as well Tree diagrams — two-stage experiments with and without replacement Without replacement — how the second probability changes after the first draw Venn diagrams and set notation — union, intersection, complement and n(A) Conditional probability — the probability of one event given another
Probability results you need to know
The probability scale. Every probability is between 0 and 1. If your answer is above 1, something has gone wrong. The complement. P(not A) = 1 − P(A). This is often the quickest route, particularly for "at least one". Mutually exclusive events. P(A or B) = P(A) + P(B), when A and B cannot both happen. Independent events. P(A and B) = P(A) × P(B), when one does not affect the other. The general addition rule. P(A or B) = P(A) + P(B) − P(A and B). Expected frequency. Expected number = probability × number of trials. At least one. P(at least one) = 1 − P(none). Far quicker than adding the cases. Without replacement. After one item is removed, both the numerator and the denominator change. A bag of 5 red from 12 becomes 4 red from 11. Conditional probability. P(B given A) is worked out from the situation after A has happened.
How to use it
Choose Foundation or Higher, then pick a topic. The engine generates a question, you type your answer, and it marks it straight away — fractions, decimals and percentages are all accepted where they are equal. Tree diagrams are drawn with the actual probabilities on the branches. Signing in saves your accuracy per topic to your GCSE skill tree.
More GCSE Maths revision
Probability shares its fractions with number and its diagrams with statistics, so the three reinforce each other. Every topic and your progress across all of them is on the revision hub. All of our revision engines are free to use.