# Relative Frequencies and Experimental Probabilities

In this worksheet, students calculate the relative frequency or experimental probability of an event happening.

Key stage:  KS 4

Curriculum topic:  Probability

Curriculum subtopic:  Calculate the Probability of Independent and Dependent Combined Events

Difficulty level:

### QUESTION 1 of 10

Probabilities can be estimated from the results of an experiment.

We calculate the relative frequency of an event happening by working out the number of times it happened in relation to the total number of trials.

On the top (numerator) of the fraction, we place the number of times an option we are looking for has happened.

On the bottom (denominator) of the fraction, we place the total number of times we have carried out the experiment.

Example

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  This experiment was repeated many times.

The results were as follows.

Red        58

Blue        32

Green     10

Calculate the relative frequency that a blue ball was drawn out?

Estimate the probability of a green ball being drawn out in future.

The experiment was carried out 58 + 32 + 10 = 100 times.

32 out of 100 blue balls were drawn out.

This is a relative frequency of 32/100 = 8/25

10 out of 100 green balls were drawn out.

This is a relative frequency of 10/100 = 1/10

Experimental probability of drawing out a green ball = 1/10

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  The experiment was repeated several times.

The results were as follows.

Red        48

Blue        32

Green     20

Calculate the relative frequency that a red ball was drawn out?

Give your answer as a fraction in its lowest terms in the form a/b.

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  The experiment was repeated several times.

The results were as follows.

Red        32

Blue        32

Green     20

Calculate the relative frequency that a green ball was drawn out?

Give your answer as a fraction in its lowest terms in the form a/b.

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  The experiment was repeated several times.

The results were as follows.

Red        32

Blue        32

Green     20

Calculate the expected probability that a blue ball will be drawn out next?

Give your answer as a fraction in its lowest terms in the form a/b.

A die was thrown and the score was noted down before it was rethrown again.  The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the relative frequency that a six was thrown?

Give your answer as a fraction in its lowest terms in the form a/b.

A die was thrown and the score was noted down before it was thrown again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the relative frequency that a six was thrown?

Give your answer as a fraction in its lowest terms in the form a/b.

A die was thrown and the score was noted down before it was thrown again.  The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the relative frequency that a four was thrown?

Give your answer as a fraction in its lowest terms in the form a/b.

A die was thrown and the score was noted down before it was thrown again.  The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the expected probability of throwing a five next.

Give your answer as a fraction in its lowest terms in the form a/b.

A spinner was spun and the score was noted down before it was spun again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 7 8 19 22 21 23 24 25 18 22

Calculate the relative frequency of a three being spun.

Give your answer as a fraction in its lowest terms in the form a/b.

A spinner was spun and the score was noted down before it was spun again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 7 8 19 22 21 23 24 25 18 22

Calculate the expected probability of spinning a five next.

Give your answer as a fraction in its lowest terms in the form a/b.

A spinner was spun and the score was noted down before it was spun again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 7 8 19 22 21 23 24 25 18 22

Calculate the expected probability of spinning a seven next.

Give your answer as a fraction in its lowest terms in the form a/b.

• Question 1

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  The experiment was repeated several times.

The results were as follows.

Red        48

Blue        32

Green     20

Calculate the relative frequency that a red ball was drawn out?

Give your answer as a fraction in its lowest terms in the form a/b.

12/25
EDDIE SAYS
The experiment is carried out 100 times.
48/100 reduces to 12/25
• Question 2

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  The experiment was repeated several times.

The results were as follows.

Red        32

Blue        32

Green     20

Calculate the relative frequency that a green ball was drawn out?

Give your answer as a fraction in its lowest terms in the form a/b.

5/21
EDDIE SAYS
The experiment is carried out 84 times.
20/84 reduces to 5/21
• Question 3

A ball was drawn out of a bag and it's colour was noted down before it was replaced.  The experiment was repeated several times.

The results were as follows.

Red        32

Blue        32

Green     20

Calculate the expected probability that a blue ball will be drawn out next?

Give your answer as a fraction in its lowest terms in the form a/b.

8/21
EDDIE SAYS
The experiment is carried out 84 times.
32/84 reduces to 8/21
• Question 4

A die was thrown and the score was noted down before it was rethrown again.  The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the relative frequency that a six was thrown?

Give your answer as a fraction in its lowest terms in the form a/b.

1/6
EDDIE SAYS
The experiment is carried out 23 + 22 + 21 + 24 + 20 + 22 = 132 times.
22/132 reduces to 1/6
• Question 5

A die was thrown and the score was noted down before it was thrown again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the relative frequency that a six was thrown?

Give your answer as a fraction in its lowest terms in the form a/b.

1/6
EDDIE SAYS
The experiment is carried out 23 + 22 + 21 + 24 + 20 + 22 = 132 times.
22/132 reduces to 1/6
• Question 6

A die was thrown and the score was noted down before it was thrown again.  The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the relative frequency that a four was thrown?

Give your answer as a fraction in its lowest terms in the form a/b.

2/11
EDDIE SAYS
The experiment is carried out 23 + 22 + 21 + 24 + 20 + 22 = 132 times.
24/132 reduces to 2/11
• Question 7

A die was thrown and the score was noted down before it was thrown again.  The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 23 22 21 24 20 22

Calculate the expected probability of throwing a five next.

Give your answer as a fraction in its lowest terms in the form a/b.

5/33
EDDIE SAYS
The experiment is carried out 23 + 22 + 21 + 24 + 20 + 22 = 132 times.
20/132 reduces to 5/33
• Question 8

A spinner was spun and the score was noted down before it was spun again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 7 8 19 22 21 23 24 25 18 22

Calculate the relative frequency of a three being spun.

Give your answer as a fraction in its lowest terms in the form a/b.

7/58
EDDIE SAYS
The experiment is carried out 19 + 22 + 21 + 23 + + 24 + 25 + 18 + 22 = 174 times.
21/174 reduces to 7/58
• Question 9

A spinner was spun and the score was noted down before it was spun again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 7 8 19 22 21 23 24 25 18 22

Calculate the expected probability of spinning a five next.

Give your answer as a fraction in its lowest terms in the form a/b.

4/29
EDDIE SAYS
The experiment is carried out 19 + 22 + 21 + 23 + + 24 + 25 + 18 + 22 = 174 times.
24/174 reduces to 4/29
• Question 10

A spinner was spun and the score was noted down before it was spun again. The experiment was repeated several times.

The results were as follows.

 Score frequency 1 2 3 4 5 6 7 8 19 22 21 23 24 25 18 22

Calculate the expected probability of spinning a seven next.

Give your answer as a fraction in its lowest terms in the form a/b.

3/29
EDDIE SAYS
The experiment is carried out 19 + 22 + 21 + 23 + + 24 + 25 + 18 + 22 = 174 times.
18/174 reduces to 3/29
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