# 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:

### QUESTION 1 of 10

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.

The largest a probability can be is...

I roll a normal dice. What is the probability I get the number 1?

(Give your answer as a fraction in the form a/b)

I roll a normal dice. What is the probability I get the number 6?

(Give your answer as a fraction in the form a/b)

I roll a normal dice. What is the probability I get a prime number?

(Give your answer as a fraction in the form a/b)

1 2 3 4 5 6

A bag contains 7 red and 3 black balls.

What is the probability of pulling out a blue ball?

A bag contains 7 red and 3 black balls.

Which of these is the probability of pulling out a black ball.

3/7

3/10

Match the following situations with the correct probability

## Column B

Rolling a number less than 3 on a normal dice
1/3
Flipping a coin and getting a head
1
Rolling a normal dice and getting a square number
1/3
Getting a number less than 7 on a normal dice
1/2

In the intro, we said that probabilites can be written as a fraction, decimal or percentage

What is the probability of throwing a coin and getting a head?

## Column B

Rolling a number less than 3 on a normal dice
1/3
Flipping a coin and getting a head
1
Rolling a normal dice and getting a square number
1/3
Getting a number less than 7 on a normal dice
1/2

True or False.

The probability it will rain tomorrow is 1.4

True

False

A bag contains 7 red and 3 black balls.

What is the probability that I pull out a red or a black ball?

• Question 1

The largest a probability can be is...

1
EDDIE SAYS
We can't go higher than 1 (this means certain)
• Question 2

I roll a normal dice. What is the probability I get the number 1?

(Give your answer as a fraction in the form a/b)

1/6
EDDIE SAYS
There is only one way to get this but there are 6 outcomes.
• Question 3

I roll a normal dice. What is the probability I get the number 6?

(Give your answer as a fraction in the form a/b)

1/6
EDDIE SAYS
The common mistake people make here is to put 6 as the numerator. Remember you are looking for how many ways you can get the 6, not that it is the six. There is only one way to get this but there are 6 outcomes.
• Question 4

I roll a normal dice. What is the probability I get a prime number?

(Give your answer as a fraction in the form a/b)

1 2 3 4 5 6

3/6
1/2
EDDIE SAYS
The first thing we need to work out is how many primes I have. If you work through the numbers 1 2 3 4 5 6 I can see there are 3 primes There are three ways to get a prime and there are 6 outcomes. Don't forget that you can cancel this fraction down to 1/2
• Question 5

A bag contains 7 red and 3 black balls.

What is the probability of pulling out a blue ball?

0
0/6
EDDIE SAYS
This can\'t happen, there aren\'t any blue balls. Our probability would be 0/10 which works out as 0 We know this is impossible and that it has a probability of 0. (This is why the scale starts at 0)
• Question 6

A bag contains 7 red and 3 black balls.

Which of these is the probability of pulling out a black ball.

3/10
EDDIE SAYS
The common mistake people make with these questions is that they use the incorrect number for the denominator. It there are 3 black and 7 red balls. There are 10 possible outcomes in total.
• Question 7

Match the following situations with the correct probability

## Column B

Rolling a number less than 3 on a...
1/3
Flipping a coin and getting a hea...
1/2
Rolling a normal dice and getting...
1/3
Getting a number less than 7 on a...
1
EDDIE SAYS
The two that catch people here are the square numbers and the number less than 7. For the square numbers, remember that a square is the answer to a number x itself. For the number less than 7 on a dice, there are 6 ways this can happen and 6 outcomes in total. This gives 6/6 which equals 1. This is why the probability scale ends at 1
• Question 8

In the intro, we said that probabilites can be written as a fraction, decimal or percentage

What is the probability of throwing a coin and getting a head?

EDDIE SAYS
This is just a little FDP conversion question. If you aren't confident about this, there's a worksheet on it.
• Question 9

True or False.

The probability it will rain tomorrow is 1.4

False
EDDIE SAYS
This has to be false because the probability is bigger than 1. Can something be more likely than certain?
• Question 10

A bag contains 7 red and 3 black balls.

What is the probability that I pull out a red or a black ball?

1
EDDIE SAYS
There are 10 balls and 10 different ways I can satisfy this. The probability will be 10/10 which equals 1 This is the link between certain and 1.
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