  # Use Two Event Probability

In this worksheet, students practise listing all the outcomes of multiple events and using them to find probabilities. Key stage:  KS 4

GCSE Subjects:   Maths

GCSE Boards:   AQA, Eduqas, Pearson Edexcel, OCR,

Curriculum topic:   Probability

Curriculum subtopic:   Probability Basic Probability and Experiments

Difficulty level:   #### Worksheet Overview

When you are finding the probability of a single event, it is fairly straightforward to find the probability of something happening.

But what about when there are multiple events happening. When I introduce this in school, I start by asking how many things could happen if I rolled two dice and I always get the (incorrect) answer 12.

To solve problems like this, we need to consider all the outcomes and list them systematically.

If I roll a 1 on the first die, there are 6 things that could happen on the second die.

If I roll a 2 on the first die, there are 6 things that could happen on the second die.

etc etc

Is there a quick way?

Yep, there certainly is. If you have 6 outcomes on the first thing and 6 on the second thing, there will be 6 x 6 = 36 outcomes

Multiply the amount of outcomes for each event to get the total number of event.

Example 1: I throw a coin and roll a dice. list all the possible outcomes.

We need to do this logically.

If I throw a head on the coin, I could get the numbers 1 - 6 on the dice.

H1 H2 H3 H4 H5 H6

If I throw a tail on the coin, I could get the number 1 - 6 on the dice

T1 T2 T3 T4 T5 T6

As a double check, I have 2 outcomes on the coin and 6 on the dice. This means I should have 2 x 6 = 12 outcomes. (And I do!)

Example 2: I throw a coin and roll a dice. what is the probability I get a head and an even number?

Our first step here is to list all the outcomes.

H1 H2 H3 H4 H5 H6

T1 T2 T3 T4 T5 T6

We can now identify which ones satisfy our condition (head and even)

H1 H2 H3 H4 H5 H6

T1 T2 T3 T4 T5 T6

We can see there are 3 outcomes that satsify the condition and 12 in total.

This gives a probability of 3/12 which simplifies to 1/4

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