Relative frequency

The working out of probabilities through some given

evidence.

Relative frequency means probability so the answers must

be between 0 and 1.

Relative Frequency

Example

A spinner with five edges numbered 1 to 5 is spun 20 times and the results are shown

below.

1 4 3 3 4 5 1 2 1 3

4 5 1 3 4 2 2 1 5 4

Complete the table of relative frequencies below.

Number on spinner

1 2 3 4 5

Relative Frequency

Example

The Bumbleton and Stickton village football teams have played each other 50

times.

Bumbleton have won 10 times, Stickton have won 35 times, and the teams have

drawn 5 times.

Estimate the probability that Stickton will win the next match

Example

Matthew decides to try to estimate the probability that toast lands butter-side-

down when dropped.

He drops a piece of buttered toast 50 times and observes that it lands butter-side-

down 30 times.

Estimate the probability that the toast lands butter-side-down.

Example

A drawing pin can land 'point up' or 'point down' when dropped.

Jim drops a drawing pin 100 times and it lands "point up" 35 times.

Estimate the probability of the drawing-pin landing "point up"

Example

A spinner has a red sector (R) and a yellow sector (Y).

R ed

Yello w

The arrow is spun 1000 times.

The table shows the relative frequency of a red after

different numbers of spins.

Number of spins Relative frequency of a red

50 0.42

100 0.36

200 0.34

500 0.3

1000 0.32

a) How many times was a red obtained after 200 spins?

b) Which relative frequency gives the best estimate of the probability of a red? Explain your answer.

Example

A dice is suspected of bias. Here are the results of 20 throws

3 4 2 3 1 5 6 2 4 3

4 3 1 1 6 2 5 6 5 3

(a) Use these results to calculate the relative frequency of each score

Score 1 2 3 4 5 6

Relative frequency

(b) Use the relative frequency to calculate how many times you would

expect to score 3 in 60 throws of this dice.

(c) Compare your answer to part (b) with the number of times you

would expect to score 3 in 60 throws of a fair dice.