Use Two-Way Tables to Find Probabilities

There are a number of ways to find the probability of more than one event.

Some of them work really well if you have a small number of events, but can be a pain if you have a large amount of data.

What is a two-way table?

A two-way table is a table with two outcomes (one along the top and one down the side), with the total outcomes classified in the cells in the middle.

It's really useful if you  have a large amount of data and want to sort it by two classes.

Example 1:

The two-way table below shows 100 students classified by their gender, and whether they are right-handed or left-handed.

The first step is to ensure that we know what this actually means.

The number 20 in the top left cell tells us there are 20 right-handed males.

The number 31 in the bottom right cell tells us there are 31 left-handed females.

Adding up all the numbers in the grid, will tell us the total outcomes for finding the probabilities.

Note: don't add any numbers that are in the title bits - the bits in blue.

Example 2:

For the two-way table shown, I pick a student at random.

Find the probability that the student is...

a) A right-handed male

There are 20 right-handed males and 100 people in total.

This is a probability of 20/100 which cancels to 1/5

b) Female

There are 61 females in this and 100 people in total

This is a probability of 61/100

c) A left-handed girl

There are 31 left-handed girls out of the 100 in total.

This is a probability of 31/100

Let's have a go at some questions now.