# Calculate Probability of Complementary Events Using Tables

In this worksheet, students will calculate probabilities of complementary events where there are either combined events or an event that benefits from generating the sample space using a table/grid.

Key stage:  KS 3

Curriculum topic:   Probability

Curriculum subtopic:   Enumerate Sets Using Tables, Grids and Diagrams

Difficulty level:

#### Worksheet Overview

We roll two dice and add what they land on. What could help us find the probability of getting a total of no more than 10?

Well, we could generate the whole sample space (i.e. all possible outcomes) using a table!

Rolling a die has 6 possible outcomes and we roll two of them, so there are 6 x 6 = 36 possible outcomes altogether.

From the table, we can count that a whopping 33 outcomes have a total of no more than 10!

This means that the probability of getting a total of no more than 10 is:

33/36 = 11/12

But generating the whole sample space is a bit tedious - is there a faster way to calculate the probability?

Well, yes, there is!

We have only two options when it comes to getting a total of no more than 10: either we get it or we don't.

Let's remember that the probability of something not happening is 1 minus the probability of it happening.

'Not getting a total above 10' is getting at least 11.

There are three ways of getting a sum of 11 or 12:

5 + 6 = 11

6 + 5 = 11

6 + 6 = 12

This is out of 6 x 6 = 36 possible outcomes altogether.

So, the probability of getting at least 11 (i.e. not getting at most 10) is:

3/36 = 1/12

That means the probability of getting at most 10 is:

1 - 1/12 = 11/12 which is exactly what we got before!

Wasn't listing the outcomes for getting at least 11 so much faster?!

Ready to put all this into practice?

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