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

i) = {2, 4, 8, 16, 32, 64}

= {square numbers}

= {cube numbers}

Use this information to complete the Venn diagram.

[2]

ii) On this Venn diagram, shade the region .

[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.

 = {children in a group}
= {children who own a rabbit}
= {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

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

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  .

[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]

 = { : is a positive integer less than 20}
A = { : is an even number}
B = { : is a multiple of 3}

i) Write down .

[1]

ii) List the elements of set .

= { ............................................... } [2]

One of these 19 numbers is picked at random.

Work out the probability that this number is

iiia) not in set and not in set ,

[1]

iiib) in

[1]

iv) Complete the statement.

[1]

 = { : is a natural number 15}

= { : is a factor of 12}

= { : 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 , but not in set .

[1]

iii) Find .

[1]

iv) A number is chosen at random from .

Work out the probability that this number is in set .

[1]

= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14}
= {: is a factor of 14}
= {: is a prime number less than 14}

i) Write down the elements in set .

= { ................................................ } [2]

ii) Write down the elements in set .

= { ................................................ } [2]

iiia) Complete the Venn diagram.

[2]

 iiib) Write down  ()

[1]

 iiic) A number is chosen at random from the universal set .

Write down the probability that the number is in the set  .

[2]

= {children who go to the park}
= {children who play tennis}
= {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().

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]