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There are a number of ways to find the probabilities 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.

Its really useful if you are wanting to sort you data by two classes and you have a large amount of data.

 

Example 1: The two way table shows the 100 students split by their gender and if they are right-handed or left-handed.

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

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

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

Adding up all the numbers in the grid (don#t add any numbers that are in the title bits - the bits in blue) will tell us the total outcomes for finding the probabilities

 

Example 2: For the two way table shown, I pick a student at random, find the probability 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

 

10 questions