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AQA GCSE Maths: Probability — Practice Questions & Answers
A complete guide to GCSE probability: the probability scale and notation, theoretical and experimental probability, expected frequency, sample space diagrams, mutually exclusive and exhaustive events, the addition and multiplication rules, independent and dependent events, tree diagrams with and without replacement, Venn diagrams with set notation, and conditional probability.
178 practice questions available for this topic — here are 10 with full answers and explanations.
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Practice questions with answers
1
Multiple choice · Easy
On the probability scale, which value represents an event that is certain to happen?
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Why Probabilities range from $0$ (impossible) to $1$ (certain), so a certain event has probability $1$.
2
Multiple choice · Easy
A fair six-sided dice is rolled once. What is the probability of rolling a $4$?
$\frac{1}{6}$
$\frac{1}{4}$
$\frac{4}{6}$
$\frac{1}{3}$
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Why There is one favourable outcome out of six equally likely outcomes, so $P(4)=\frac{1}{6}$.
3
Multiple choice · Easy
A bag contains $3$ red and $7$ blue counters. One counter is taken at random. What is the probability it is red?
$\frac{3}{10}$
$\frac{3}{7}$
$\frac{7}{10}$
$\frac{1}{3}$
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Why There are $3$ red out of $10$ counters in total, so $P(\text{red})=\frac{3}{10}$.
4
Multiple choice · Easy
The probability that it rains tomorrow is $0.35$. What is the probability that it does not rain tomorrow?
$0.65$
$0.35$
$0.55$
$1.35$
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Why The probability of an event not happening is $1$ minus the probability it happens, so $1-0.35=0.65$.
5
Multiple choice · Easy
A fair coin is flipped once. Which word best describes the chance of getting heads?
Even chance
Impossible
Certain
Unlikely
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Why There are two equally likely outcomes, so heads has probability $\frac{1}{2}$, described as even chance.
6
Multiple choice · Easy
A spinner has $5$ equal sections numbered $1$ to $5$. What is the probability of spinning an even number?
$\frac{2}{5}$
$\frac{3}{5}$
$\frac{1}{5}$
$\frac{1}{2}$
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Why The even numbers are $2$ and $4$, giving $2$ outcomes out of $5$, so $P(\text{even})=\frac{2}{5}$.
7
Multiple choice · Easy
A dice is rolled $60$ times. How many times would you expect to roll a $3$?
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Why Expected frequency is probability times trials, so $\frac{1}{6}\times 60=10$.
8
Multiple choice · Easy
Two events A and B cannot both happen at the same time. What are they called?
Mutually exclusive
Independent
Exhaustive
Conditional
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Why Events that cannot occur together are mutually exclusive.
9
Multiple choice · Medium
A bag has red, green and yellow counters. $P(\text{red})=0.4$ and $P(\text{green})=0.25$. What is $P(\text{yellow})$?
$0.35$
$0.65$
$0.15$
$0.3$
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Why All probabilities sum to $1$, so $P(\text{yellow})=1-0.4-0.25=0.35$.
10
Multiple choice · Medium
A coin is flipped and a fair dice is rolled. How many outcomes are in the sample space?
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Why There are $2$ coin outcomes and $6$ dice outcomes, giving $2\times 6=12$ total outcomes.
Key terms in Probability
Probability: A measure of how likely an event is to happen, given as a number between $0$ and $1$.
Event: An outcome or set of outcomes from an experiment, such as rolling an even number.
Outcome: A single possible result of an experiment, such as getting a head when tossing a coin.
Trial: A single performance of an experiment, such as one roll of a dice.
Experiment: A repeatable process with uncertain results, such as spinning a spinner.
Sample space: The set of all possible outcomes of an experiment.
Sample space diagram: A table or grid listing all possible outcomes, often for two combined events.
Equally likely outcomes: Outcomes that each have the same chance of happening, such as the faces of a fair dice.
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