Relative Frequency Practice Questions
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Experimental Probability
The chance or occurrence of a particular event is termed its probability. The value of a probability lies between 0 and 1 which means if it is an impossible event, the probability is 0 and if it is a certain event, the probability is 1. The probability that is determined on the basis of the results of an experiment is known as experimental probability. This is also known as empirical probability.
What is Experimental Probability?
Experimental probability is a probability that is determined on the basis of a series of experiments. A random experiment is done and is repeated many times to determine their likelihood and each repetition is known as a trial. The experiment is conducted to find the chance of an event to occur or not to occur. It can be tossing a coin, rolling a die, or rotating a spinner. In mathematical terms, the probability of an event is equal to the number of times an event occurred ÷ the total number of trials. For instance, you flip a coin 30 times and record whether you get a head or a tail. The experimental probability of obtaining a head is calculated as a fraction of the number of recorded heads and the total number of tosses. P(head) = Number of heads recorded ÷ 30 tosses.
Experimental Probability Formula
The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. The formula to calculate the experimental probability is: P(E) = Number of times an event occurs/Total number of times the experiment is conducted
Consider an experiment of rotating a spinner 50 times. The table given below shows the results of the experiment conducted. Let us find the experimental probability of spinning the color - blue.
The experimental probability of spinning the color blue = 10/50 = 1/5 = 0.2 = 20%
Experimental Probability vs Theoretical Probability
Experimental results are unpredictable and may not necessarily match the theoretical results. The results of experimental probability are close to theoretical only if the number of trials is more in number. Let us see the difference between experimental probability and theoretical probability.
Experimental Probability Examples
Here are a few examples from real-life scenarios.
a) The number of cookies made by Patrick per day in this week is given as 4, 7, 6, 9, 5, 9, 5.
Based on this data, what is the reasonable estimate of the probability that Patrick makes less than 6 cookies the next day?
P(< 6 cookies) = 3/7 = 0.428 = 42%
b) Find the reasonable estimate of the probability that while ordering a pizza, the next order will not be of a pepperoni topping.
Based on this data , the reasonable estimate of the probability that the next type of toppings that would get ordered is not a pepperoni will be 15/20 = 3/4 = 75%
Related Sections
- Card Probability
- Conditional Probability Calculator
- Binomial Probability Calculator
- Probability Rules
- Probability and Statistics
Important Notes
- The sum of the experimental probabilities of all the outcomes is 1.
- The probability of an event lies between 0 and 1, where 0 is an impossible event and 1 denotes a certain event.
- Probability can also be expressed in percentage.
Examples on Experimental Probability
Example 1: The following table shows the recording of the outcomes on throwing a 6-sided die 100 times.
Find the experimental probability of: a) Rolling a four; b) Rolling a number less than four; c) Rolling a 2 or 5
Experimental probability is calculated by the formula: Number of times an event occurs/Total number of trials
a) Rolling a 4: 17/100 = 0.17
b) Rolling a number less than 4: 56/100 = 0.56
c) Rolling a 2 or 5: 31/100 = 0.31
Example 2: The following set of data shows the number of messages that Mike received recently from 6 of his friends. 4, 3, 2, 1, 6, 8. Based on this, find the probability that Mike will receive less than 2 messages next time.
Mike has received less than 2 messages from 2 of his friends out of 6.
Therefore, P(<2) = 2/6 = 1/3
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Practice Questions on Experimental Probability
Frequently asked questions (faqs), how do you find the experimental probability.
The experimental probability of an event is based on actual experiments and the recordings of the events. It is equal to the number of times an event occurred divided by the total number of trials.
What is the Experimental Probability of rolling a 6?
The experimental probability of rolling a 6 is 1/6. A die has 6 faces numbered from 1 to 6. Rolling the die to get any number from 1 to 6 is the same and the probability (of getting a 6) = Number of favorable outcomes/ total possible outcomes = 1/6.
What is the Difference Between Theoretical and Experimental Probability?
Theoretical probability is what is expected to happen and experimental probability is what has actually happened in the experiment.
Do You Simplify Experimental Probability?
Yes, after finding the ratio of the number of times the event occurred to the total number of trials conducted, the fraction which is obtained is simplified.
Which Probability is More Accurate, Theoretical Probability or Experimental Probability?
Theoretical probability is more accurate than experimental probability. The results of experimental probability are close to theoretical only if the number of trials are more in number.
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Relative Frequency
Here we will learn about relative frequency, including how to calculate it.
There are also relative frequency worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still stuck.
What is relative frequency?
Relative frequency is the number of times an event happens divided by the total number of outcomes that took place in an experiment, known as the number of trials.
To calculate the relative frequency we can use the formula,
For example,
Jo made a four-sided spinner out of a piece of card and a pencil. She spun the spinner 50 times and the spinner landed on a three 15 times. Calculate the relative frequency of the spinner landing on a three.
Relative frequency of landing on a three = \frac{15}{50} or \frac{3}{10} or 0.3 or 30\%.
The more times an experiment is carried out, the more reliable the relative frequency will be and closer to the theoretical probability.
How to calculate relative frequency
In order to calculate relative frequency:
Find the number of times the event occurs.
Find the number of trials of the experiment.
Use the formula \textbf{Relative frequency = }\frac{\textbf{frequency of event occurring}}{\textbf{total number of trials of the experiment}} Write your answer as a fraction, decimal or percentage.
Explain how to calculate relative frequency
Relative frequency worksheet
Get your free relative frequency worksheet of 20+ questions and answers. Includes reasoning and applied questions.
Related lessons on probability distribution
Relative frequency is part of our series of lessons to support revision on probability distribution . You may find it helpful to start with the main probability distribution lesson for a summary of what to expect, or use the step by step guides below for further detail on individual topics. Other lessons in this series include:
- Probability distribution
- Experimental probability
- Theoretical probability
- Expected frequency
Relative frequency examples
Example 1: calculating relative frequency.
A coin is flipped 50 times and shows heads on 22 occasions. Calculate the relative frequency of the coin showing heads.
The coin showed heads 22 times.
2 Find the number of trials of the experiment.
The coin was flipped 50 times.
3 Use the formula \textbf{Relative frequency = }\frac{\textbf{frequency of event occurring}}{\textbf{total number of trials of the experiment}} Write your answer as a fraction, decimal or percentage.
Relative frequency =\frac{22}{50}=0.44
Example 2: calculating relative frequency
A coin shows heads 15 times having been flipped 40 times. Calculate the relative frequency of the coin showing tails.
If the coin showed heads 15 times, it would have showed tails 25 times.
The coin was flipped 40 times.
Relative frequency =\frac{25}{40}=0.625
Example 3: calculating the number of trials if relative frequency is known
An experiment rolling a normal 6 -sided dice obtained the number 4 on 32 occasions.
The relative frequency of rolling a 4 was calculated as 0.2. Find the number of times the dice was rolled.
The number 4 was rolled 32 times.
This is what we need to calculate using step 3.
Use the formula \textbf{Relative frequency = }\frac{\textbf{frequency of event occurring}}{\textbf{total number of trials of the experiment}}
As we already know the relative frequency, substitute this and the frequency of rolling a 4 into the formula.
0.2=\frac{32}{\text{number of times the die was rolled}}
Rearrange the formula.
Number of times the dice was rolled =\frac{32}{0.2}=160 .
Common misconceptions
- Assuming relative frequency is equal to the theoretical probability
The relative frequency of an event is determined by the number of trials or observations. If an experiment only has a small number of trials it is possible for the relative frequency to be very different from the theoretical probability of the same event. For example – if a coin is flipped only 5 times, it is very possible for it to show heads on all 5 occasions.
- Assuming a relative frequency with few trials is a good estimate for the theoretical probability
Practice relative frequency questions
1. A coin is flipped 80 times and shows heads 50 times. Find the relative frequency for the coin showing heads, giving your answer as a fraction in its simplest form.
\frac{50}{80} simplifies to \frac{5}{8} .
2. A coin is flipped 60 times and shows tails 24 times. Find the relative frequency for the coin showing tails, giving your answer as a decimal.
3. A coin is flipped 50 times and shows heads 31 times. Find the relative frequency for the coin showing tails , giving your answer as a fraction.
If the coin shows heads 31 times it must show tails 19 times. 50-31 = 19.
4. A 3 sided spinner, numbered 1, \ 2 and 3, is spun 200 times. It lands on 1, \ 60 times, and lands on 2, \ 85 times. Calculate the relative frequency of the spinner landing on 3. Give your answer as a fraction in its simplest form.
5. A normal 6- sided dice is rolled 150 times. The relative frequency of the die landing on 2 is 0.36. How many times did the die land on 2?
6. A 4- sided spinner numbered 1 to 4 is spun n times in an experiment. The spinner lands on 3, 76 times. The relative frequency of the spinner landing on 3 was calculated as \frac{19}{75}. Find the value of n.
Relative frequency GCSE questions
1. A school recorded the number of times different fruits were bought by students for their lunch.
Find the relative frequency of
(a) a student buying an apple.
(b) a student not buying grapes.
Evidence of a fraction with denominator 150 .
\frac{53}{150} or 0.353… or equivalent.
\frac{121}{150} or 0.8066… or equivalent.
2. Jenny is doing an experiment to test the fairness of a 6- sided dice. She rolled the dice 12 times and got the following results.
Jenny claims that the dice is not fair based on her results.
(a) Explain why Jenny may not be correct.
Simon repeats the experiment with the same die but rolls the die 36 times. His results are below.
(b) Using all the information available find the relative frequency of rolling a 4 on the dice.
“Jenny has not rolled the die many times” or “if she rolled the die more times her results would be more accurate”
\frac{9}{48} or 0.1875 or equivalent.
3. A coin is flipped 500 times and shows tails 324 times.
Find the relative frequency of the coin showing heads .
0.352 or equivalent.
Learning checklist
You have now learned how to:
- Calculate the relative frequency of an event occurring from a probability experiment
The next lessons are
- Describing probability
- How to calculate probability
- Combined events probability
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Example 1: finding an experimental probability distribution. A 3− 3− sided spinner numbered 1,2, 1, 2, and 3 3 is spun and the results are recorded. Find the probability distribution for the 3− 3− sided spinner from these experimental results. Draw a table showing the frequency of each outcome in the experiment.
As n increases, the relative frequency tends toward the theoretical probability. Figure \(\PageIndex{2}\) shows a graph of experimental probabilities as n gets larger and larger. The dashed yellow line is the theoretical probability of rolling a 4, which is \(\dfrac{1}{6}\) \(\approx\) 0.1667.
A probability, relative frequency, percentage, and proportion are all different words for the same concept. Probability answers can be given as percentages, decimals, or reduced fractions. Suppose that the experiment is rolling a die. Compute the probability of rolling a 4.
The Corbettmaths Practice Questions on Relative Frequency. Welcome; Videos and Worksheets; Primary; 5-a-day. 5-a-day GCSE 9-1; ... experimental probability. Practice ...
Example 1: finding an experimental probability distribution. A 3 3 sided spinner numbered 1,2, 1,2, and 3 3 is spun and the results recorded. Find the probability distribution for the 3 3 sided spinner from these experimental results. Draw a table showing the frequency of each outcome in the experiment.
The experimental probability of an event is based on the number of times the event has occurred during the experiment and the total number of times the experiment was conducted. Each possible outcome is uncertain and the set of all the possible outcomes is called the sample space. The formula to calculate the experimental probability is: P (E ...
Calculate the relative frequency of the spinner landing on a three. Relative frequency of landing on a three = \frac{15}{50} or \frac{3}{10} or 0.3 or 30\%. The more times an experiment is carried out, the more reliable the relative frequency will be and closer to the theoretical probability.
Example 2: Experimental Probability and Relative Frequency A coin was tossed 200 times and the number of tails observed was 102. Calculate the relative frequency of getting a heads.
Experimental probability or empirical probability is also sometimes called “relative frequency,” but you’ll usually find the term reserved for applications like the Relative Frequency Table. It’s probably more accurate to say that experimental probability is the experimental process of figuring out probabilities (including the results ...
Relative frequency is used to estimate probabilities from experimental data. For a certain number of trials, the probability of ‘success’ is given as. e.g. If you flip an unfair coin 50 times and it lands on heads 20 times then you would use relative frequency to estimate the probability of the coin landing on heads as.