Two-Way Tables (Cambridge (CIE) IGCSE International Maths)
Revision Note
Written by: Mark Curtis
Reviewed by: Dan Finlay
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Two Way Tables
What are two-way tables?
Two-way tables are tables that compare two types of characteristics
For example, a college of 55 students has two year groups (Year 12 and Year 13) and two language options (Spanish and German)
The two-way table is shown:
Spanish
German
Year 12
15
10
Year 13
5
25
How do I find probabilities from a two-way table?
Draw in the totals of each row and column
Include an overall total in the bottom-right corner
It should be the sum of the totals above, or to its left (both work)
For the example above:
Spanish
German
Total
Year 12
15
10
25
Year 13
5
25
30
Total
20
35
55
Use this to answer probability questions
If a random student is selected from the whole college, it will be out of 55
The probability a student selected from the college studies Spanish and is in Year 12 is
The probability a student selected from the college studies Spanish is
If a random student is selected from a specific category, the denominator will be that category total
The probability a student selected from Year 13 studies Spanish is
Examiner Tips and Tricks
Check your row and column totals add up to the overall total, otherwise all your probabilities will be wrong!
Worked Example
At an art group, children are allowed to choose between colouring, painting, clay modelling and sketching.
A total of 60 children attend and are split into two classes: class A and class B.
12 of class A chose the activity colouring and 13 of class B chose clay modelling.
A total of 20 children chose painting and a total of 15 chose clay modelling.
8 of the 30 children in class A chose sketching, as did 4 children in class B.
(a) Construct a two-way table to show this information.
Read through each sentence and fill in the numbers that are given
| Colouring | Painting | Clay modelling | Sketching | Total |
Class A | 12 |
|
| 8 | 30 |
Class B |
|
| 13 | 4 |
|
Total |
| 20 | 15 |
| 60 |
Use the row and column totals to fill in any obvious missing numbers
| Colouring | Painting | Clay modelling | Sketching | Total |
Class A | 12 |
| 15 - 13 = 2 | 8 | 30 |
Class B |
|
| 13 | 4 | 60 - 30 = 30 |
Total |
| 20 | 15 | 8 + 4 = 12 | 60 |
Use the row and column totals again to find the last few numbers
| Colouring | Painting | Clay modelling | Sketching | Total |
Class A | 12 | 30 - 12 - 2 - 8 = 8 | 2 | 8 | 30 |
Class B | 30 - 12 - 13 - 4 = 1 | 20 - 8 = 12 | 13 | 4 | 30 |
Total | 12 + 1 = 13 | 20 | 15 | 12 | 60 |
Write out your final answer
| Colouring | Painting | Clay modelling | Sketching | Total |
Class A | 12 | 8 | 2 | 8 | 30 |
Class B | 1 | 12 | 13 | 4 | 30 |
Total | 13 | 20 | 15 | 12 | 60 |
(b) Find the probability that a randomly selected child
(i) chose colouring,
(ii) is in class A, who chose sketching.
(i) We are not interested in whether the child is in class A or B
A total of 13 children chose colouring, out of 60 children
P(colouring) =
(ii) 8 children in class A chose sketching
There are 60 children to select from
P(class A and sketching) =
(c) A child in class B is selected at random. Find the probability they chose painting.
As we are only selecting from class B, this will be out of 30 (rather than the total of 60)
12 in class B chose painting
P(painting, from class B only) =
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