Solve Probability Problems Using Two-way Tables

What is your favourite subject?

 

 

A survey was conducted amongst 150 students to determine their favourite subjects: maths, English, or science.

 

We know:

Out of 110 boys, 22 prefer science and 62 maths.

100 students prefer maths and 42 English.

 

What is the probability that a student selected at random is a girl who prefers English?

 

 

We have so many numbers here - finding this probability sounds a little complicated, doesn't it?

But it doesn't have to be if we organise this data into a two-way table:

 

	Maths	English	Science	Total
Boys	62	26	22	110
Girls	38	16	16	70
Total	100	42	38	180

 

We found the numbers we were not given by using the totals.

 

For example, we were told that out of 110 boys, 22 prefer science and 62 maths.

So the number of boys who prefer English is 110 - 22 - 62 = 26

 

We want to find the probability that a student selected at random is a girl who prefers English.

From the table we can see that there are 16 girls who prefer English.

 

Since there are 180 students in total, the probability that a student selected at random is a girl who prefers English is 16/180 = 4/45

 

Didn't having the two-way table make it so much easier?!

 

 

Let's put this all into practice!