Set Notation & Probability Diagrams (Cambridge (CIE) IGCSE Maths: Core): Exam Questions

i) $\mathcal{E}$= {2, 4, 8, 16, 32, 64}

$A$ = {square numbers}

$B$ = {cube numbers}

Use this information to complete the Venn diagram.

[2]

ii) On this Venn diagram, shade the region $P\cup Q$.

[1]

In a group of 40 students,

• 24 students like football

• 19 students like cricket

• 10 students like football but not cricket.

Complete the Venn diagram.

$\mathcal{E}$ = {children in a group}
$R$= {children who own a rabbit}
$H$ = {children who own a hamster}

There are 40 children in the group.
19 children own a rabbit.
27 children own a hamster.

Complete the Venn diagram.

Write down $n\left(R\cap H\right).$

The Venn diagram shows information about the number of students in a class who like apples ($A$) and bananas ($B$).

i) Work out the number of students in the class.

[1]

ii) Work out the number of students who like bananas.

[1]

iii) Work out  $n\left(A\cup B\right)$.

[1]

iv) How many more students like apples than like bananas?

[1]

v) One of the students is chosen at random.

Find the probability that this student does not like apples and does not like bananas.

[1]

The table gives some information about the numbers of visitors at a leisure centre one day.

i) Complete the table.

[1]

ii) Work out how many more child visitors than adult visitors there are.

[1]

iii) Write down the fraction of visitors that are adults. Give your answer in its lowest terms.

[2]

iv) Write the ratio number of males : number of females. Give your answer in its simplest form.

..................... : ................... [2]

v) One of these visitors is selected at random. Find the probability that this visitor is a male child.

[1]

$\xi$ = {$x:x$ is a natural number less than 15}

$A$ = {3, 6, 9, 10, 12}

$B$= {2, 3, 4, 5, 9, 11, 13, 14}

Complete the Venn diagram.

Find $\mathrm{n}\left(A\cap B\right)$.

Find $\mathrm{n}\left(A\cup B\text{'}\right)$.

$\xi$= {positive integers less than 16}

$X$ = {prime numbers}

$Y$={multiples of 3}

Use this information to complete the Venn diagram.

List all the elements of $X\cap Y$

Find $\mathrm{n}\left(Y\text{'}\right)$

$\mathcal{E}$ = {$x$ : $x$ is a positive integer less than 20}
A = {$x$ : $x$ is an even number}
B = {$x$ : $x$ is a multiple of 3}

i) Write down $\mathrm{n}\left(A\right)$.

[1]

ii) List the elements of set $B$.

$B$= { ............................................... } [2]

One of these 19 numbers is picked at random.

Work out the probability that this number is

iiia) not in set $A$ and not in set $B$,

[1]

iiib) in $A\cup B$

[1]

iv) Complete the statement.

$A\cap B=\left\{x:x\mathrm{is}...............................\right\}$

[1]

$\mathcal{E}$ = {$x$ : $x$ is a natural number $⩽$15}

$F$ = {$x$ : $x$ is a factor of 12}

$O$ = {$x$ : $x$ is an odd number}

i) Complete the Venn diagram to show the elements of these sets.

[2]

ii) Write down one number that is in set $O$, but not in set $F$.

[1]

iii) Find $\mathrm{n}\left(F\cup O\right)$.

[1]

iv) A number is chosen at random from $\mathcal{E}$.

Work out the probability that this number is in set $O$.

[1]

$\mathcal{E}$ = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
$F$ = {$x$: $x$ is a factor of 14}
$P$ = {$x$: $x$ is a prime number less than 14}

i) Write down the elements in set $F$.

$F$ = { ................................................ } [2]

ii) Write down the elements in set $P$.

$P$ = { ................................................ } [2]

iiia) Complete the Venn diagram.

[2]

 iiib) Write down  $\mathrm{n}$($F\cap P$)

[1]

 iiic) A number is chosen at random from the universal set $\mathcal{E}$.

Write down the probability that the number is in the set  $F\cup P$ .

[2]

$\mathcal{E}$= {children who go to the park}
$T$= {children who play tennis}
$G$ = {children who play golf}

120 children go to the park.
50 play tennis.
75 play golf.
25 do not play tennis or golf.

Complete the Venn diagram.

[2]

Find n($T\cap G$).

The 262 students at a college each study one of the languages shown in the table.

Complete the table.

[3]

Find the probability that

i) a girl, chosen at random, studies Spanish,

[1]

ii)a boy, chosen at random, studies French or Italian,

[1]

iii)a student, chosen at random, does not study German.

[1]

Ali rolls a fair six-sided dice labelled 1 to 6.

Ali gets a point when the dice lands on a number greater than 4.

Let $M$ denote the event that Ali's dice lands on a number greater than 4 when rolled.

He rolls the dice twice.

Complete the tree diagram.

Calculate the probability that he gets a point twice.

Calculate the probability that he lands on 4 or less at least once.

Two bags, A and B, each contain green beads and red beads only.

The probability of taking a green bead at random from bag A is 0.6.

The probability of taking a green bead at random from bag B is 0.2.

A student takes one bead at random from bag A and one bead from bag B.

Complete the tree diagram.

Find the probability he gets one of each colour.