Two Way Tables
Like Venn Diagrams, two way tables are a visual way of representing information.
The two way table below represents how many numbers between 2-20 are even or a multiple of 3.
It's called a two way table because we can read information from it in two directions. If read across each row, we can tell how many numbers are even or not. If we read down each column, we can tell how many numbers are multiples of 3 or not.
Where a particular row and column overlap, these are how many numbers between 2 and 20 satisfy both categories. For example, there are 7 numbers that are even but not a multiple of 3.
Notice that the number in the bottom right cell (19) is how many numbers there are altogether between 2 and 20.
Worked Examples
QUESTION 1
Dave surveyed all the students in Year $12$12 at his school and summarised the results in the following table:
| Play netball | Do not play netball | Total | |
|---|---|---|---|
| Height$\ge$≥$170$170 cm | $46$46 | $73$73 | $119$119 |
| Height$<$<$170$170 cm | $20$20 | $39$39 | $59$59 |
| Total | $66$66 | $112$112 | $178$178 |
What percentage of Year $12$12 students whose height is less than $170$170 cm play netball?
Round your answer to two decimal places.
What fraction of the students from Year $12$12 do not play netball?
QUESTION 2
In a biology study, the appearance of an animal when carrying a certain gene is recorded. Assume that all animals must cary Gene $A$A or Gene $B$B but not both.
| Gene $A$A | Gene $B$B | |
|---|---|---|
| Light fur | $36$36 | $27$27 |
| Dark fur | $28$28 | $x$x |
If, out of all the animals, the proportion carrying Gene A and having light fur is $\frac{4}{19}$419, what is the value of $x$x?
Enter each line of working as an equation.
QUESTION 3
$36$36 students were asked whether or not they were allergic to nuts and dairy. The two way table is provided below.
| Allergic to nuts | Not allergic to nuts | |
|---|---|---|
| Allergic to dairy | $10$10 | $6$6 |
| Not allergic to dairy | $6$6 | $14$14 |
How many students are allergic to nuts?
How many students are allergic to nuts or dairy, or both?
How many students are allergic to at most one of the two things?