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Videos, examples and solutions to help GCSE Maths students learn about relative frequency and probability.

Relative frequency is the number of times something happens divided by the number of total outcomes. We can use relative frequency to estimate probability.

**Relative Frequency**

GCSE Module 1 Topic 07

Example:

An ordinary 6-sided dice is repeatedly thrown 10 times. The number of sixes are counted for each set of ten throws.

a) Complete the relative frequency table

b) Complete the relative frequency graph

c) Does the results suggest that the dice is biased towards the number six?

**Relative Frequency and experimental probability (GCSE Maths)**

Example:

1. Twenty pupils each shuffle a pack of coloured cards and choose a card at random.

The colour of the card is recorded for each pupil.

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

(b) Use the results to calculate how many times you would expect a blue card if 100 pupils each choose a card at random.

2. Kali has a spinner with coloured sections of equal size.

She wants to know the probability that her spinner lands on pink.

She spins it 100 times and calculates the relative frequency of pink every 10 spins.

Her results are shown on the graph.

a) Using the graph to calculate the number of times that the spinner landed on pink

i) after the first 10 spins,

ii) after the first 50 spins.

b) From the graph, estimate the probability of the spinner landing on pink.

**Relative frequency**

Example:

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

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

b) Use the relative frequency to calculate how many times you would expect to score 3 in 60 throws of the die.

c) Compare your answer to part b) with the number you would expect 3 in 60 throws of a fair dice.

**Relative Frequency Probability**

There are three ways to make a probability statement.

1) Theoretical Probability

2) Experimental Probability (relative frequency probability)

3) Subjective Probability

Example:

Consider the frequency distribution for a sample of patients in an orthopedic clinic.

Chance experiment: A receptionist notes the height of the next person that enters the clinic.

Let E be the event of observing a patient in the 5'6" ≤ h ≤ 6'0" height interval.

What is P(E)?

**Relative Frequency**

How to work out relative frequency?

**Relative Frequency and Probability**

Explore the relationship between Relative Frequency and Probability.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

More GCSE Maths Lessons

More Probability Lessons

Probability Worksheets

Probability Games

Videos, examples and solutions to help GCSE Maths students learn about relative frequency and probability.

Relative frequency is the number of times something happens divided by the number of total outcomes. We can use relative frequency to estimate probability.

GCSE Module 1 Topic 07

Example:

An ordinary 6-sided dice is repeatedly thrown 10 times. The number of sixes are counted for each set of ten throws.

a) Complete the relative frequency table

b) Complete the relative frequency graph

c) Does the results suggest that the dice is biased towards the number six?

Example:

1. Twenty pupils each shuffle a pack of coloured cards and choose a card at random.

The colour of the card is recorded for each pupil.

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

(b) Use the results to calculate how many times you would expect a blue card if 100 pupils each choose a card at random.

2. Kali has a spinner with coloured sections of equal size.

She wants to know the probability that her spinner lands on pink.

She spins it 100 times and calculates the relative frequency of pink every 10 spins.

Her results are shown on the graph.

a) Using the graph to calculate the number of times that the spinner landed on pink

i) after the first 10 spins,

ii) after the first 50 spins.

b) From the graph, estimate the probability of the spinner landing on pink.

Example:

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

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

b) Use the relative frequency to calculate how many times you would expect to score 3 in 60 throws of the die.

c) Compare your answer to part b) with the number you would expect 3 in 60 throws of a fair dice.

There are three ways to make a probability statement.

1) Theoretical Probability

2) Experimental Probability (relative frequency probability)

3) Subjective Probability

Example:

Consider the frequency distribution for a sample of patients in an orthopedic clinic.

Chance experiment: A receptionist notes the height of the next person that enters the clinic.

Let E be the event of observing a patient in the 5'6" ≤ h ≤ 6'0" height interval.

What is P(E)?

How to work out relative frequency?

Explore the relationship between Relative Frequency and Probability.

Rotate to landscape screen format on a mobile phone or small tablet to use the **Mathway** widget, a free math problem solver that **answers your questions with step-by-step explanations**.

You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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