Cambridge · IGCSE Maths 0580

Cambridge IGCSE Maths: Probability — Practice Questions & Answers

Q: Which value could NOT be the probability of an event?

$1.2$. All probabilities lie on the scale from $0$ to $1$ inclusive, so $1.2$ is impossible.

Q: A fair six-sided die is rolled once. What is the probability of getting a $4$?

$\frac{1}{6}$. There is one favourable outcome out of six equally likely outcomes, so $P(4)=\frac{1}{6}$.

Q: The probability that it rains tomorrow is $0.3$. What is the probability that it does NOT rain?

$0.7$. The complement is $1-0.3=0.7$.

Q: A bag has $5$ red and $3$ blue balls. One ball is taken at random. What is the probability it is blue?

$\frac{3}{8}$. There are $3$ blue out of $8$ total, so $P(\text{blue})=\frac{3}{8}$.

Q: A spinner is spun $200$ times and lands on green $50$ times. What is the relative frequency of green?

$0.25$. Relative frequency is $\frac{50}{200}=0.25$.

Q: The probability of winning a game is $\frac{1}{5}$. If the game is played $40$ times, what is the expected number of wins?

$8$. Expected frequency is $\frac{1}{5}\times 40=8$.

Q: A card is drawn from a standard pack of $52$. What is the probability it is a heart?

$\frac{1}{4}$. There are $13$ hearts in $52$ cards, so $\frac{13}{52}=\frac{1}{4}$.

Q: Two mutually exclusive events have $P(A)=0.4$ and $P(B)=0.5$. What is $P(A \text{ or } B)$?

$0.9$. For mutually exclusive events the addition rule gives $P(A)+P(B)=0.4+0.5=0.9$.

Q: The numbers $1$ to $10$ are written on cards. One is chosen at random. What is the probability it is even?

$\frac{1}{2}$. There are $5$ even numbers in $10$, so $\frac{5}{10}=\frac{1}{2}$.

Q: A bag has $4$ red and $6$ green sweets. Two are taken with replacement. What is the probability both are red?

$\frac{4}{25}$. With replacement the probability stays the same, so $\frac{4}{10}\times\frac{4}{10}=\frac{16}{100}=\frac{4}{25}$.

Probability measures how likely an event is, on a scale from 0 (impossible) to 1 (certain). This topic covers writing probabilities as fractions, decimals or percentages, finding the probability of single and combined events, using relative frequency from experiments and expected frequency for predictions, applying the addition and multiplication rules, distinguishing independent from dependent events, drawing tree diagrams with and without replacement, and using Venn diagrams with set notation to handle 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

Which value could NOT be the probability of an event?

$1.2$
$0$
$0.45$
$1$

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2 Multiple choice · Easy

A fair six-sided die is rolled once. What is the probability of getting a $4$?

$\frac{1}{6}$
$\frac{1}{4}$
$\frac{4}{6}$
$\frac{1}{3}$

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3 Multiple choice · Easy

The probability that it rains tomorrow is $0.3$. What is the probability that it does NOT rain?

$0.7$
$0.3$
$0.6$
$1.3$

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4 Multiple choice · Easy

A bag has $5$ red and $3$ blue balls. One ball is taken at random. What is the probability it is blue?

$\frac{3}{8}$
$\frac{5}{8}$
$\frac{3}{5}$
$\frac{1}{3}$

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5 Multiple choice · Easy

A spinner is spun $200$ times and lands on green $50$ times. What is the relative frequency of green?

$0.25$
$0.5$
$0.4$
$0.2$

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6 Multiple choice · Easy

The probability of winning a game is $\frac{1}{5}$. If the game is played $40$ times, what is the expected number of wins?

$8$
$5$
$20$
$32$

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7 Multiple choice · Easy

A card is drawn from a standard pack of $52$. What is the probability it is a heart?

$\frac{1}{4}$
$\frac{1}{13}$
$\frac{1}{2}$
$\frac{13}{39}$

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8 Multiple choice · Easy

Two mutually exclusive events have $P(A)=0.4$ and $P(B)=0.5$. What is $P(A \text{ or } B)$?

$0.9$
$0.2$
$0.1$
$0.45$

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9 Multiple choice · Easy

The numbers $1$ to $10$ are written on cards. One is chosen at random. What is the probability it is even?

$\frac{1}{2}$
$\frac{1}{10}$
$\frac{2}{10}$
$\frac{1}{5}$

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10 Multiple choice · Medium

A bag has $4$ red and $6$ green sweets. Two are taken with replacement. What is the probability both are red?

$\frac{4}{25}$
$\frac{2}{15}$
$\frac{8}{10}$
$\frac{12}{90}$

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Key terms in Probability

Probability: A measure of how likely an event is to occur, between $0$ and $1$.

Experiment: A process or trial whose outcome is uncertain.

Outcome: A single possible result of an experiment.

Event: A set of one or more outcomes of an experiment.

Sample space: The set of all possible outcomes of an experiment.

Equally likely outcomes: Outcomes that each have the same chance of occurring.

Theoretical probability: Probability based on equally likely outcomes, $\frac{\text{favourable outcomes}}{\text{total outcomes}}$.

Experimental probability: Probability estimated from the results of repeated trials.

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Cambridge IGCSE Maths: Probability — Practice Questions & Answers

Practice questions with answers

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Key terms in Probability

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