Browse Venn diagrams & set notation

35 questions at your level

DifficultyAllLevel 1Level 2Level 3Level 4Level 5

Venn diagrams

13 questions

LessonNot started
100100 people were asked which of apples, bananas and cherries they had eaten in the last week.
  • 5252 had eaten apples,
  • 4141 had eaten bananas,
  • 3939 had eaten cherries,
  • 2020 had eaten apples and bananas,
  • 1717 had eaten apples and cherries,
  • 1515 had eaten bananas and cherries,
  • 99 had eaten none of the three fruits.
(a) Work out how many of the 100100 people had eaten all three fruits.

(b) Work out how many of the 100100 people had eaten exactly one of the three fruits.
●●●●●Level 56 marksStart
A youth club has 6464 members. Every member does at least one of drama and dance.

2828 members do drama but not dance.

The number of members who do both drama and dance is 33 times the number who do dance but not drama.

(a) Work out how many members do dance.

(b) Work out how many members do drama.
●●●●●Level 55 marksStart

Set notation

11 questions

LessonNot started
ξ\xi is the set of the 6060 students in Year 11 at a school.

AA is the set of students who have a part-time job.

BB is the set of students who play a musical instrument.

n(A)=34n(A) = 34, n(B)=29n(B) = 29 and n(A′∩B′)=8n(A' \cap B') = 8.

(a) Find n(A∪B)n(A \cup B).

(b) Find n(A∩B)n(A \cap B).

(c) Find n(A∩B′)n(A \cap B').
●●●●●Level 55 marksStart
ξ={1,2,3,4,5,6,7,8,9,10,11,12}\xi = \{1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12\}

A={multiples of 4}A = \{\text{multiples of }4\}

B={even numbers}B = \{\text{even numbers}\}

C={multiples of 5}C = \{\text{multiples of }5\}

(a) Explain why A⊂BA \subset B.

(b) Write down n(A∩C)n(A \cap C).

(c) List the members of (B∪C)′(B \cup C)'.
●●●●●Level 55 marksStart

Probability from Venn diagrams

12 questions

LessonNot started
120120 people were asked whether they own a bicycle (AA) and whether they have a gym membership (BB). The Venn diagram shows the results.ξ48AB421812One of the 120120 people is chosen at random.

(a) Find P(A∩B)P(A \cap B).

(b) Determine whether the events AA and BB are independent. You must show your working.

(c) Ben says that AA and BB are mutually exclusive. Is Ben correct? Give a reason for your answer.
●●●●●Level 56 marksStart
The Venn diagram shows the probabilities for two events AA and BB. The probability that neither AA nor BB occurs is xx.ξxAB0.250.180.27(a) Find the value of xx.

(b) Find P(A′)P(A').

(c) Given that BB occurs, find the probability that AA also occurs.
●●●●●Level 56 marksStart