  # Using Equally Likely Outcomes

In this worksheet, students find probabilities using equally likely outcomes. 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

You should be familiar with the idea of using words (Impossible, Unlikely, Evens, Likely, Certain) to describe probabilities.

The issue with these is when we want to compare probabilities. Using words can be used to say which probability is higher if, for example, one was likely and one was certain.

But what happens if we want to compare two likely events?

This is when using numbers to describe probabilities come in. The one we are using today works for equally likely outcomes.

What are equally likely outcomes?

There are a number of things in real life that have more than 1 thing that could happen when each one has an equal chance of happening.

For example;

If you throw a coin, it is equally likely you will get a head or a tail.

If you roll a normal dice, there are 6 things that could come up (1,2,3,4,5,6) and each has an equal chance of happening.

If you pull a card at random out of a deck, there are 52 cards and you have an equal chance of getting any one of them.

How to write probabilities as a number?

There is a lovely little formula we can use here.

P(event) =
 Favourable outcomes Total outcomes

Favourable outcomes are just the things we want to happen

Total outcomes is the total number of things that could happen

Example: If I roll a normal dice, What is the chance I get a 5?

There is only one favourable outcome here as the number 5 only appears once

There are 6 outcomes in total

P(5 on a dice) =
 1 6

Example: If I roll a normal dice, What is the chance I get a even?

There are three favourable outcome here as there are 3 even numbers on a dice

There are 6 outcomes in total

P(5 on a dice) =
 3 6

Don't forget as well that you could cancel this down.

Do probabilities have to be a fraction?

Most probabilities are given as fractions, but there's nothing wrong with changing the fractions into either a decimal or a percentage if you want to.

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