 # Use Tables to Record Probability

In this worksheet, students practise recording probability using a table. 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

When we are dealing with probability, sometimes it can get really confusing so we need to find a way to record the probabilities that allows us to read and use the probabilities.

Example 1: A bag contains only Red, Yellow, Blue and Green balls. Complete the table to show the probability of picking out a green ball.

 Red Yellow Blue Green Probability 0.6 0.1 0.1

The trick here is to remember that probabilities must add up to 1. To find the probability of green, we just have to take all the numbers we know away from 1.

1 - 0.6 - 0.1 - 0.1 = 0.2

Example 2: A bag contains only blue, yellow and green balls.

There are twice as many blues as yellows.

There are four times as many green balls as blue balls.

Find the probability of picking out a blue ball.

The way we approach this initially is to draw a table.

 Blue Yellow Green Probability

The issue we have is we only know the amount of balls relative to each other. To deal with this, we use algebra.

We can start by noticing that the smallest amount will be the yellow, we call this x

If we have twice as many blue as yellow, we have 2x blue

We have four times as many green as blue, this gives (4 x 2x = ) 8x green balls.

We can now fill in the table

 Blue Yellow Green Probability 2x x 8x

Once again, we can look at the fact that the probabilities here add up to 1.

2x + x + 8x = 1

11x = 1

x = 0.091...

Our last step is to find the probability we are asked for.

We are looking for the probability that we pick out a blue ball.

P(blue) = 2x = 2 x 0.091 = 0.18==

A bag contains only red, yellow, blue and green balls.

Find the probability of picking out a green ball.

 Red Yellow Blue Green Probability 0.3 0.5 0.1

A bag contains only red, yellow, blue and green balls.

There are the same amount of yellow balls and blue balls.

Complete the probability table.

 Red Yellow Blue Green Probability 0.2 A B 0.3

 Probability A B

A fair five side dice is rolled. Complete the probability table.

 1 2 3 4 5 Probability A B C D E

 Probability 1 2 3 4 5

There are 4 types of counter in a bag, labelled A,B,C and D.

Fill in the table to find the probability of picking out a counter labelled D.

 A B C D Probability 0.2 0.4 0.25

A bag contains 6 red, 4 blue, 5 green and 5 yellow balls.

Match the outcomes to the probabilities.

## Column B

Red
0.3
Blue
0.25
Green
0.2
Yellow
0.25

A bag contains only red, yellow and blue balls.

There are twice as many blue as red balls and five times as many yellow as red balls.

Complete the probability table.

 Red Yellow Blue Probability x

 Probability Yellow Blue

A bag contains only blue, red and yellow balls.

There are the same amount of red and blue balls and half as many yellow balls as red balls.

Find the probability of...

 Probability Blue Red Yellow

A weighted dice is thrown.

The probability of getting either a 1,2 or 3 is the same.

The probability of getting a 4 is double the probability of a 1

The probability of getting a 5 is three times the probability of a 1

The probability of getting a 6 is twice the probability of a 1/

Find the probability of getting a 5.

A weighted dice is thrown.

The probability of getting either a 1,2 or 3 is the same.

The probability of getting a 4 is double the probability of a 1

The probability of getting a 5 is three times the probability of a 1

The probability of getting a 6 is twice the probability of a 1/

What is the least likely outcome?

Select all that apply.

1

2

3

4

5

6

A weighted spinner is thrown.

The chance of getting a red is twice as likely as a blue.

The chance of getting a yellow is twice as likely as a red

Throwing a green is 3/4 as likely as throwing a yellow.

Find the difference between the probability of getting a blue and the probability of getting a yellow.

• Question 1

A bag contains only red, yellow, blue and green balls.

Find the probability of picking out a green ball.

 Red Yellow Blue Green Probability 0.3 0.5 0.1

0.1
EDDIE SAYS
Remember that the probabilities must add up to 1. If we add up the ones we know, we get 0.9 This leaves the probability of green as...
• Question 2

A bag contains only red, yellow, blue and green balls.

There are the same amount of yellow balls and blue balls.

Complete the probability table.

 Red Yellow Blue Green Probability 0.2 A B 0.3

 Probability A B
EDDIE SAYS
Remember that the probabilities must add up to 1. If we add up the ones we know, we get 0.5 We are told that there are the same amount of yellow and blue, this means the probabilities must be the same.
• Question 3

A fair five side dice is rolled. Complete the probability table.

 1 2 3 4 5 Probability A B C D E

 Probability 1 2 3 4 5
EDDIE SAYS
The key thing to notice here is that the dice is fair, this means that all the outcomes are the same. As the five must be equal AND add to 1, we must divide 1 by 5.
• Question 4

There are 4 types of counter in a bag, labelled A,B,C and D.

Fill in the table to find the probability of picking out a counter labelled D.

 A B C D Probability 0.2 0.4 0.25

0.15
EDDIE SAYS
If we add up all the probabilities we know, we get 0.85 As all the probabilities must add up to 1, this gives 1 - 0.85
• Question 5

A bag contains 6 red, 4 blue, 5 green and 5 yellow balls.

Match the outcomes to the probabilities.

## Column B

Red
0.3
Blue
0.2
Green
0.25
Yellow
0.25
EDDIE SAYS
If we look at the formula for probability for each option... P = Favourable outcomes/Expected outcomes P(red) = 6/20 = 0.3 You can then just complete this for the rest of the options.
• Question 6

A bag contains only red, yellow and blue balls.

There are twice as many blue as red balls and five times as many yellow as red balls.

Complete the probability table.

 Red Yellow Blue Probability x

 Probability Yellow Blue
EDDIE SAYS
If the probabilty of red is x (because we don't know how many red balls there are) Blue will be twice this and yellow will be 5 times this.
• Question 7

A bag contains only blue, red and yellow balls.

There are the same amount of red and blue balls and half as many yellow balls as red balls.

Find the probability of...

 Probability Blue Red Yellow
EDDIE SAYS
When we are dealing with questions of this form, we make the smallest probability X, This gives P(Y) = X and P(R) = P(B) = 2x Adding these together gives 5x which we know is equal to 1. This makes x = 0.2.
• Question 8

A weighted dice is thrown.

The probability of getting either a 1,2 or 3 is the same.

The probability of getting a 4 is double the probability of a 1

The probability of getting a 5 is three times the probability of a 1

The probability of getting a 6 is twice the probability of a 1/

Find the probability of getting a 5.

0.3
EDDIE SAYS

If we create a table for this, we get...

 1 2 3 4 5 6 Probability x x x 2x 3x 2x

Adding together the probabilities gives 10x = 1

this makes x = 0.1

We are looking for the probability of getting a 5, we need to find 3x...

• Question 9

A weighted dice is thrown.

The probability of getting either a 1,2 or 3 is the same.

The probability of getting a 4 is double the probability of a 1

The probability of getting a 5 is three times the probability of a 1

The probability of getting a 6 is twice the probability of a 1/

What is the least likely outcome?

Select all that apply.

1
2
3
EDDIE SAYS

If we create a table for this, we get...

 1 2 3 4 5 6 Probability x x x 2x 3x 2x
We can see from this that the least likely outcomes is 1,2 or 3
• Question 10

A weighted spinner is thrown.

The chance of getting a red is twice as likely as a blue.

The chance of getting a yellow is twice as likely as a red

Throwing a green is 3/4 as likely as throwing a yellow.

Find the difference between the probability of getting a blue and the probability of getting a yellow.

0.3
EDDIE SAYS

For this, we can start by creating and filling in a probability table.

 Red Blue Yellow Green Probability 2x x 4x 3x

This gives the equation 10x = 0.1 and we can say that x = 0.1

The Probability of getting blue is x which equals 0.1

The Probability of getting a yellow is 4x = 0.4

This means the difference of these is...

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