Everything Maths Grade 10

Worked example 5: Venn diagrams

QUESTION

Consider the set of diamonds removed from a deck of cards. A random card is selected from the set of diamonds.

• Write down the sample space,S, for the experiment.


• What is the value ofn(S)?


• Consider the following two events:
  
  
  • P: An even diamond is chosen
  
  
  • R: A royal diamond is chosen
    Represent the sample spaceSand eventsPandRusing a Venn diagram.
  
  
  
  

SOLUTION

Step 1: Write down the sample space S

S=fA; 2; 3; 4; 5; 6; 7; 8; 9; 10;J;Q;Kg

Step 2: Write down the value ofn(S)

n(S) = 13

Step 3: Draw the Venn diagram

6

10

Q

2

4

8

J

K

7 3

5 9

A

P R

S

Exercise 14 – 3:

1.A group of learners are given the following Venn diagram:

4

3

10

15

14

9

8

2 13

12

11 5 1

7

6

A B

(A[B)′

A\B

S

The sample space can be described asfn:n εZ; 1 n 15 g.

Chapter 14. Probability 479