Two-way tables show information about two characteristics, one being presented in the columns and one presented in the rows.
For example, a table may show the amount of boys and girls who preferred football or rugby.
You will need to able to construct two-tables as well as use them to calculate probabilities of specific events occurring.
The following two-way table shows information about the hair colour of 100 children:
What do the values mean?
There are \textcolor boys with black hair.
There are \textcolor children with blonde hair.
There are \textcolor girls.
There are \textcolor children overall.
Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC Cambridge iGCSE Edexcel iGCSE 
You may be asked to complete incomplete two-way tables.
The following two-way table shows information about the hair colour of another 100 children, with some missing values:
In this table, we need to find the missing values, \textcolor and \textcolor :
\textcolor : we know there are 100 children overall, and 51 of these are boys, so we can find how many girls there are overall:
100-51=49\\ \textcolor = 49
Level 4-5 GCSE KS3 AQA Edexcel OCR WJEC Cambridge iGCSE Edexcel iGCSETwo-way tables also allows us to calculate probabilities .
The following two-way table shows information about how 50 people travel to school or work:
Examples of calculating probability:
From the table, we can see 11 under 25 ‘s walk to school or work, out of a possible 50 people.
Therefore, the probability is \dfrac .
From the table, we can see 7 people in total take the bus, out of a possible 50 people.
Therefore, the probability is \dfrac .
Level 4-5 GCSE AQA Edexcel OCR WJEC Cambridge iGCSE Edexcel iGCSE 
We can also calculate conditional probabilities from two-way tables.
The following two-way table shows information about how 50 people travel to school or work:
Conditional probability example:
We are given that the person is over 25 , and as there are 25 people over this age, this is the total number of possible people that can be chosen.
From the table, we can see 12 over 25 ‘s drive to school or work.
This gives us a probability of 12 out of a total 25 people:
