It is common in the GCSE exam that questions come up where you are given information about two variables (i.e. gender and eye colour) and you are asked to work out the value of one specific part of this information (i.e. how many males have blue eyes)
To solve these questions, the easiest way is to use a two-way table.
Example 1: Complete the two-way table.
Blue | Brown | Green | Total | |
Male | 6 | 3 | 14 | |
Female | 5 | |||
Total | 8 | 30 |
To complete this, we just need to make each row and column add up to the total that is given.
To start, we need to find the row or column that has only one missing.
If you keep repeating this, eventually you will get...
Blue | Brown | Green | Total | |
Male | 6 | 5 | 3 | 14 |
Female | 6 | 5 | 5 | 16 |
Total | 12 | 10 | 8 | 30 |
Example 2:
100 people are asked if they swim, cycle or run.
40 of the people were female
26 of the 47 runners were female
30 people swim
10 men were cyclists
a) Find the number of people who cycled.
Step 1 here is to draw a two-way table and enter the totals that we know.
Swim | Run | Cycle | Total | |
Male | 10 | |||
Female | 26 | 40 | ||
Total | 30 | 47 | 100 |
Once we have this, we can fill in the rest of the information...
Swim | Run | Cycle | Total | |
Male | 29 | 21 | 10 | 60 |
Female | 1 | 26 | 13 | 40 |
Total | 30 | 47 | 23 | 100 |
From this, it is quite easy to see that the total amount of cyclists is 23.
b) Given that I choose a woman, what is the probability she will be a runner?
Be careful with this one, we are limiting this to women only so the probability will be out of 40.
26 of the women are runners which makes our probability 26/40 which cancels to 13/20