Two Way Tables (Edexcel GCSE Maths: Foundation)

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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 15 over 55
      • The probability a student selected from the college studies Spanish is 20 over 55
    • 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 5 over 30

Examiner Tip

  • 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) = bold 13 over bold 60

(ii)
8 children in class A chose sketching
There are 60 children to select from

P(class A and sketching) = bold 8 over bold 60 bold equals bold 2 over bold 15

 

(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) = bold 12 over bold 30 bold equals bold 2 over bold 5 

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Mark

Author: Mark

Expertise: Maths

Mark graduated twice from the University of Oxford: once in 2009 with a First in Mathematics, then again in 2013 with a PhD (DPhil) in Mathematics. He has had nine successful years as a secondary school teacher, specialising in A-Level Further Maths and running extension classes for Oxbridge Maths applicants. Alongside his teaching, he has written five internal textbooks, introduced new spiralling school curriculums and trained other Maths teachers through outreach programmes.