Grade 10 Maths · Probability · Read Venn diagram notation

Read Venn diagram notation Grade 10

Match set notation such as A B, A B and A' to the regions of a Venn diagram and to words, for example (A B)' means in neither A nor B.

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Practice · Siyavula Grade 10 Maths · Ex 14.7 · 2 marks

A group of learners are given the following Venn diagram:
The sample space can be described as

{n : n \in Z, 1 \leq n \leq 15}

.
They are asked to identify the complementary event set of

B

, also known as

B^{'}

. They get stuck, and you offer to help them find it. Which of the following sets best describes the event set of

B^{'}

?
-

{1; 5; 13; 14}

{2; 3; 4; 6; 10; 11; 12}

{3; 4; 6; 11; 12}

(2)

Work it out on paper first. Then mark yourself with the memo, one tick at a time.

More questions: read venn diagram notation

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3. Practice · Siyavula Grade 10 Maths · Ex 14.7 · 3 marks
Given the following Venn diagram:
The sample space can be described as ${n : n \in Z, 1 \leq n \leq 15}$ .
Are $A^{'}$ and $B^{'}$ mutually exclusive?(3)
Show the memo (3 ticks)Memo
1. ✓
  A complement $A^{'} = {2}$
  1 mark · Read Venn diagram notation
2. ✓
  B complement $B^{'} = {2; 4; 5; 7; 9; 12; 13; 15}$
  1 mark · Read Venn diagram notation
3. ✓
  AnswerBoth contain $2$ , so $A^{'}$ and $B^{'}$ are not mutually exclusive.
  1 mark · Use the addition rule
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue
4. Practice · NavyBlue · 2 marks
In a class of $40$ learners, $22$ play soccer, $15$ play netball and $6$ play both.
Let $F$ be the event "plays soccer" and $N$ the event "plays netball". Write the event "plays soccer or netball" in set notation and find its probability.(2)
Show the memo (2 ticks)Memo
1. ✓
  Notation $F \cup N$
  1 mark · Read Venn diagram notation
2. ✓
  Probability $P (F \cup N) = \frac{16 + 6 + 9}{40} = \frac{31}{40}$
  1 mark · Find probability from a Venn diagram
5. Practice · NavyBlue · 2 marks
A number is chosen at random from $S = {1; 2; 3; \dots; 20}$ . $A$ is the event that the number is a multiple of $3$ and $B$ is the event that it is even.
Describe $B^{'}$ in words and calculate $P (B^{'})$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  In words $B^{'}$ : the number is odd (not even)
  1 mark · Read Venn diagram notation
2. ✓
  Probability $P (B^{'}) = \frac{10}{20} = \frac{1}{2}$
  1 mark · Find probability from a Venn diagram
6. Practice · Siyavula Grade 10 Maths · Ex 14.7 · 2 marks
Given the following Venn diagram:
The sample space can be described as ${n : n \in Z, 1 \leq n \leq 15}$ .
Are $(A \cup B)^{'}$ and $A \cup B$ mutually exclusive?(2)
Show the memo (2 ticks)Memo
1. ✓
  The two sets $A \cup B = {1; 2; 5; 7; 8; 9; 11; 14; 15}$
  $(A \cup B)^{'} = {3; 4; 6; 10; 12; 13}$
  1 mark · Read Venn diagram notation
2. ✓
  AnswerThey have no elements in common, so yes, they are mutually exclusive.
  1 mark · Use the addition rule
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue

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