~ GCSE Mathematics – Probability 3 ~
Estimating Probability using Relative frequency
You can estimate probability from the relative frequency of an outcome given by:
relative frequency of an outcome 
Colour
Outcome
me
frequency of the outcome
total number of trials
Tally for 10 trials
Frequency for
10 trials
Relative
frequency
(fraction)
Experimental
probability
(decimal)
success
fail
Total
Experiment
number
Number of
successful
outcomes out
of 10
Cumulative
total of
number
of trials
1
10
2
20
3
30
4
40
5
50
6
60
7
70
8
80
9
90
10
100
1
Cumulative total
of successful
number of
outcomes
Relative frequency
(fraction)
Estimated
probability
(decimal)
y
0.9
0.8
relative
frequency
0.7
0.6
0.5
0.4
0.3
0.2
Total number
of trials
0.1
x
10
20
30
40
50
60
70
80
90
100
marian.harrington@abingdon-witney.ac.uk
~ GCSE Mathematics – Probability 3 ~
Example
The table shows the number of times a spinner landed on one of
A, B, C or D in 100 spins.
Lands
on
a) What is the experimental probability of the spinner
landing on B?
b) Do you think the spinner is fair? Explain.
Total out of
100 spins
A
18
B
38
C
24
D
20
c) If the same spinner was spun 400 times, how many times would you expect it to land on B?
Predicting the number of outcomes of an event
The predicted number of outcomes of an event = Probability x number of trials
Q1. If an ordinary coin is spun 150 times, how many times would you expect it to land on a head?
Q2. Larry is going to roll a dice 90 times. Work out an estimate for the number of times it will land
on:
a) 6
b) an even number
c) 1 or 2
Q3. The probability that a seed will grow into a flower is 0.85.
If 800 seeds are planted, how many seeds would you expect to grow into flowers?
Q4. Phoebe has a 4 sided dice. The sides of the dice are numbered 1,2,3 & 4. The table shows the
probabilities that the dice will land on 1, 2 or 3.
Number
Probability
1
2
3
0.25
0.1
0.35
4
Phoebe rolls the dice 200 times. Estimate the number of times that the dice will land on 4.
Q5.
If the probability of picking a red sweet from a bag of 50 sweets is 0.1, how many red sweets are in
the bag?
Additional practice: Edexcel 16+ book p. 269 Ex. 23D
marian.harrington@abingdon-witney.ac.uk