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Prob. distribution

Experimental prob.

## Experimental probability

Here you will learn about experimental probability, including using the relative frequency and finding the probability distribution.

Students will first learn about experimental probability as part of statistics and probability in 7 th grade.

## What is experimental probability?

Experimental probability is the probability of an event happening based on an experiment or observation.

To calculate the experimental probability of an event, you calculate the relative frequency of the event.

Relative frequency =\cfrac{\text{frequency of event occurring}}{\text{total number of trials of the experiment}}

You can also express this as R=\cfrac{f}{n} where R is the relative frequency, f is the frequency of the event occurring, and n is the total number of trials of the experiment.

If you find the relative frequency for all possible events from the experiment, you can write the probability distribution for that experiment.

The relative frequency, experimental probability, and empirical probability are the same thing and are calculated using the data from random experiments. They also have a key use in real-life problem-solving.

For example, Jo made a four-sided spinner out of cardboard and a pencil.

She spun the spinner 50 times. The table shows the number of times the spinner landed on each of the numbers 1 to 4. The final column shows the relative frequency.

The relative frequencies of all possible events will add up to 1.

This is because the events are mutually exclusive.

See also: Mutually exclusive events

## [FREE] Probability Check for Understanding Quiz (Grade 7 to 12)

Use this quiz to check your grade 7 to 12 students’ understanding of probability. 15+ questions with answers covering a range of 7th to 12th grade probability topics to identify areas of strength and support!

## Experimental probability vs theoretical probability

You can see that the relative frequencies are not equal to the theoretical probabilities you would expect if the spinner was fair.

If the spinner is fair, the more times an experiment is done, the closer the relative frequencies should be to the theoretical probabilities.

In this case, the theoretical probability of each section of the spinner would be 0.25, or \cfrac{1}{4}.

Step-by-step guide: Theoretical probability

## Common Core State Standards

How does this relate to 7 th grade math?

- Grade 7 – Statistics & Probability (7.SP.C.5) Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around \cfrac{1}{2} indicates an event that is neither unlikely nor likely, and a probability near 1 indicates a likely event.

## How to find an experimental probability distribution

In order to calculate an experimental probability distribution:

Draw a table showing the frequency of each outcome in the experiment.

Determine the total number of trials.

Write the experimental probability (relative frequency) of the required outcome(s).

## Experimental probability examples

Example 1: finding an experimental probability distribution.

A 3- sided spinner numbered 1, \, 2, and 3 is spun and the results are recorded.

Find the probability distribution for the 3- sided spinner from these experimental results.

A table of results has already been provided. You can add an extra column for the relative frequencies.

2 Determine the total number of trials.

3 Write the experimental probability (relative frequency) of the required outcome(s).

Divide each frequency by 110 to find the relative frequencies.

## Example 2: finding an experimental probability distribution

A normal 6- sided die is rolled 50 times. A tally chart was used to record the results.

Determine the probability distribution for the 6- sided die. Give your answers as decimals.

Use the tally chart to find the frequencies and add a row for the relative frequencies.

The question stated that the experiment had 50 trials. You can also check that the frequencies add up to 50.

Divide each frequency by 50 to find the relative frequencies.

## Example 3: using an experimental probability distribution

A student made a biased die and wanted to find its probability distribution for use in a game. They rolled the die 100 times and recorded the results.

By calculating the probability distribution for the die, determine the probability of the die landing on a 3 or a 4.

The die was rolled 100 times.

You can find the probability of rolling a 3 or a 4 by adding the relative frequencies for those numbers.

P(3\text{ or }4)=0.22+0.25=0.47

Note: P(\text{Event }A) means the probability of event A occurring.

Alternatively, it is only necessary to calculate the relative frequencies for the desired events but by calculating all of the relative frequencies and finding the sum of these values, your solution should equal 1.

The frequency of rolling a 3 or a 4 is 22+25=47.

As the total frequency is 100, the relative frequency is \cfrac{47}{100}=0.47.

## Example 4: calculating the relative frequency without a known frequency of outcomes

A research study asked 1,200 people how they commute to work. 640 travel by car, 174 use the bus, and the rest walk. Determine the relative frequency of someone walking to work.

Writing the known information into a table, you have

You currently do not know the frequency of people who walk to work. You can calculate this as you know the total frequency.

The number of people who walk to work is equal to

1200-(640+174)=386.

You now have the full table,

The total frequency is 1,200.

Divide each frequency by the total number of people (1,200), you have

The relative frequency of someone walking to work is 0.3216.

## How to find a frequency using an experimental probability

In order to calculate a frequency using an experimental probability:

Determine the experimental probability of the event.

Multiply the total frequency by the experimental probability.

## Example 5: calculating a frequency

A dice was rolled 300 times. The experimental probability of rolling an even number is \cfrac{27}{50}. How many times was an even number rolled?

The experimental probability is \cfrac{27}{50}.

An even number was rolled 162 times.

## Example 6: calculating a frequency

A bag contains different colored counters. A counter is selected at random and replaced back into the bag 240 times. The probability distribution of the experiment is given below.

Determine the total number of times a blue counter was selected.

As the events are mutually exclusive, the sum of the probabilities must be equal to 1.

This means that you can determine the value of x.

1-(0.4+0.25+0.15)=0.2

The experimental probability (relative frequency) of a blue counter is 0.2.

Multiplying the total frequency by 0.2, you have

240 \times 0.2=48

A blue counter was selected 48 times.

## Teaching tips for experimental probability

- Relate probability to everyday situations, such as the chance of getting heads or tails when flipping a fair coin, to make the concept more tangible.
- Rather than strictly using worksheets, let students conduct their own experiments, such as rolling dice or drawing marbles from a bag, to collect data and compute probabilities.
- Emphasize that in mathematics, experimental probability is based on actual trials or experiments, as opposed to theoretical probability which is based on possible outcomes.
- Teach students how to record the results of an experiment systematically and use them to calculate probabilities. Use charts or tables to help visualize the data.
- Discuss events that cannot occur, such as rolling a 7 with a single six-sided die. Explain that the probability of impossible events is always 0. This helps students understand the concept of probability in a broader context.

## Easy mistakes to make

- Forgetting the differences between theoretical and experimental probability It is common to forget to use the relative frequencies from experiments for probability questions and use the theoretical probabilities instead. For example, they may be asked to find the probability of a die landing on an even number based on an experiment and the student will incorrectly answer it as 0.5.
- Thinking the relative frequency is an integer The relative frequency is the same as the experimental probability. This value is written as a fraction, decimal, or percentage, not an integer.
- Assuming future results will be the same Students might think that if an experiment yields a certain probability on one day, the results will be the same the next day. Explain that while probabilities are consistent over time in theory, each set of trials can have different outcomes due to randomness, and variations can occur from day to day.

## Related probability distribution lessons

- Probability distribution
- Expected frequency

## Practice experimental probability questions

1. A coin is flipped 80 times and the results are recorded.

Determine the probability distribution of the coin.

As the number of tosses is 80, dividing the frequencies for the number of heads and the number of tails by 80, you have

2. A 6- sided die is rolled 160 times and the results are recorded.

Determine the probability distribution of the die. Write your answers as fractions in their simplest form.

Dividing the frequencies of each number by 160, you get

3. A 3- sided spinner is spun and the results are recorded.

Find the probability distribution of the spinner, giving your answers as decimals to 2 decimal places.

By dividing the frequencies of each color by 128 and simplifying, you have

4. A 3- sided spinner is spun and the results are recorded.

Find the probability of the spinner not landing on red. Give your answer as a fraction.

Add the frequencies of blue and green and divide by 128.

5. A card is picked at random from a deck and then replaced. This was repeated 4,000 times. The probability distribution of the experiment is given below.

How many times was a club picked?

6. Find the missing frequency from the probability distribution.

The total frequency is calculated by dividing the frequency by the relative frequency.

## Experimental probability FAQs

Experimental probability is the likelihood of an event occurring based on the results of an actual experiment or trial. It is calculated as the ratio of the number of favorable outcomes to the total number of trials.

To calculate experimental probability, you calculate the relative frequency of the event: \text{Relative frequency}=\frac{\text{Frequency of event occurring}}{\text{Total number of trials of the experiment}}

Experimental Probability is based on actual results from an experiment or trial. Theoretical Probability is based on the possible outcomes of an event, calculated using probability rules and formulas without conducting experiments.

It helps us understand how likely events are in real-world scenarios based on actual data. For example, it can be used to predict outcomes in various fields such as social science, medicine, finance, and engineering.

## The next lessons are

- Units of measurement
- Represent and interpret data

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## Privacy Overview

Trending Resource : 40+ Activities for the First Week of School

## Engaging Probability Games and Activities

This blog post contains Amazon affiliate links. As an Amazon Associate, I earn a small commission from qualifying purchases.

Looking for some fun ways to teach probability? Check out this collection of 9 engaging probability games and activities that are perfect for any unit on data analysis and probability.

## Probability Games for the Middle School or High School Classroom

When I first started teaching, the only way I knew to review probability with my students was to give them multiple-choice questions like they would likely see on the state test at the end of the year. These questions usually revolved around weather events or selling school raffle tickets. My students were not enthused.

I decided to switch things up and have my students experience experimental probability and theoretical probability for themselves by having them participate in various probability games. These games are suitable for the middle school or high school classroom. I have even received emails from college math professors using these games with their students.

Every student will enjoy embracing the excitement of chance and challenge as they explore the important concepts of theoretical and experimental probability. My goal is to share games that are easy to play, simple to explain, and use supplies that teachers already have in their classroom such as linking cubes , a deck of cards, or dice .

This Blocko Probability game is a fun way to introduce the difference between experimental and theoretical probability to students.

I play the game with linking cubes with my students, but you could actually use any collection of small items.

## Probability Bingo

Probability Bingo is not your typical bingo game! It is designed to help students build an understanding of probability by thinking through all of the possible combinations of colors that can be rolled.

Students fill their bingo boards based on the color combinations they think will appear the most. The winner is the person who fills out their entire bingo board first.

## Greedy Pig Dice Game

I have been playing this greedy pig dice game with my students to practice probability since I learned it while student teaching!

All you need for this game is a set of dice !

## Teaching Probability with Deal or No Deal

Students will enjoy calculating probabilities while playing through a game of Deal or No Deal ! So many different probability concepts can be discussed while you work through a simulation of the popular tv game show.

There are many other game shows that you could pull ideas from for other probability-based lessons.

## Left Center Right Game

There is so much probability to explore with the Left Center Right Dice game . I love playing a few rounds of Left Center Right to kick off my probability units!

## Probability Exploration Activities

When it comes to teaching probability, hands-on activities are the secret ingredient to making math lessons memorable and impactful. In this section, we’ll delve into a variety of engaging probability activities that you can seamlessly integrate into your middle or high school math curriculum.

These probability activities use easy-to-find supplies such as linking cubes , hex nuts, rope, and cardstock .

## Mystery Box Probability Activity

Can your students use their knowledge of probability to determine the contents of the mystery box using the relative frequency of the colors?

## Hex Nut Probability Activity

All you need for this fun and engaging hex nut probability activity are hex nuts, empty soda bottles, and a plastic ring.

## Probability with Cuboctahedrons

Your students will enjoy building cuboctahedrons and using them to explore a fun probability question!

## Marriage Probability Activity

My high school students really enjoyed exploring the probability behind an old fable regarding the likelihood of getting married in the next year.

## More Resources for Teaching Probability

Sarah Carter teaches high school math in her hometown of Coweta, Oklahoma. She currently teaches AP Precalculus, AP Calculus AB, and Statistics. She is passionate about sharing creative and hands-on teaching ideas with math teachers around the world through her blog, Math = Love.

## Similar Posts

## Russian Fable for Marriage Probability Activity

## 3 Circle Venn Diagram Template

## Left Center Right Dice Game

## Blocko Probability Game

## Experimental vs theoretical probability

I can see the impact of sample size and compare theoretical probabilities to experimental ones.

## Lesson details

Key learning points.

- Different sample sizes can impact the experimental probabilities
- As the sample size increases, the experimental probabilities approach the theoretical probabilities
- A larger sample size is more likely to show a truer estimation of the underlying probability

## Common misconception

Pupils may assume that it possible to determine whether a coin (or other object/game) is biased by conducting an experiment with a small number of trials.

The greater the number of trial that an experiment contains, the closer the relative frequency of an outcome gets to its theoretical probability.

Trial - A trial is a single, pre-defined test.

Experiment - An experiment is a repetition of a trial multiple times in order to observe how often each outcome occurs.

Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

6 questions.

## Experimental Probability

What is experimental probability.

This activity allows the user to conduct probability experiments with traditional probability devices such as a spinner and dice. Studying random events with such devices and computer simulations allows you to gain familiarity with the connection between experimental and theoretical probability.

The study of probability allows mathematicians and scientists to make predictions when the outcomes of events are not certain. Probability is essential to the study and prediction of weather patterns, developing medicines, hereditary traits, and most experiments in science.

## Related Resources

- Activity Adjustable Spinner
- Activity Coin Toss
- Activity Crazy Choices Game
- Activity Racing Game with One Die
- Activity Racing Game with Two Dice
- Discussion about Equally Likely (Fair) Choice
- Discussion about Polyhedra
- Discussion about Random Number Generators
- Discussion about Theoretical Versus Experimental Probability
- Worksheet Experimental Probability Exploration Questions
- Worksheet Experimental Probability Exploration Questions (doc)

## How Do I Use This Activity?

This activity allows the user to experiment with probability by spinning a spinner or rolling dice.

## Controls and Output

Begin by choosing to use a preset spinner, make your own spinner, or use dice.

Preset Spinners

- Click on the New Spinner button to choose the type of preset spinner you would like to use.
- Set the number of spins to either 1, 5, or 10.
- Click the Spin button to spin the spinner. Your data will be collected in the window to the right of the spinner.
- Press the Clear Tally button to erase your data and begin again.

Make Your Own Spinner

- The maximum number of slices is 12 similar to a clock.
- The spinner starts out with 4 slices, one of each color.
- The black handles located at 12, 6 and 9 o'clock can be used to increase or decrease the size of a slice by clicking and dragging with the mouse.
- The black handles cannot be used to completely remove a slice, only shrink it to its smallest size of 1/12 of the whole pie.
- The white handle cannot be moved. It represents the first piece or starting point of the pie.
- The + and - buttons on the lower right-hand side can be used to add or remove a slice of a particular color.
- New slices are added at the 4 o'clock position, one sector clockwise from the white handle.
- The size of a new slice will always be 1/12 of the whole pie.
- A black handle will appear to represent the new slice. This handle can be used to adjust it's size.
- When pressing the - button to remove a slice, the first slice of the selected color clockwise from 3 o'clock is removed.
- Removing a slice will cause the adjacent clockwise slice to enlarge, taking up the empty space.
- Set the number of spins, then click the Spin button.
- You can click the New Dice button to select from a set of preset dice, or you can click the Make Dice button to create your own six-sided dice.
- When selecting from the preset list or making your own dice your selection will be applied to both dice, meaning both dice will always be identical.
- Set the number of rolls, then click the Roll Dice button.

## Description

This activity allows the user to experiment with various random number generator models such as spinners and number cubes and tally results. This activity would work well in groups of 2-3 for about 45 minutes.

## Place in Mathematics Curriculum

This activity can be used to:

- give students experience generating sets of data using random number generators.
- manipulate random number generators to see the effects on experimental probabilities.

## Standards Addressed

Statistics and probability.

- The student demonstrates a conceptual understanding of probability.
- The student demonstrates a conceptual understanding of probability and counting techniques.

## Statistics, Data Analysis, and Probability

- 3.0 Students determine theoretical and experimental probabilities and use these to make predictions about events

## Seventh Grade

- Investigate chance processes and develop, use, and evaluate probability models.

## Conditional Probability and the Rules of Probability

- Understand independence and conditional probability and use them to interpret data
- Use the rules of probability to compute probabilities of compound events in a uniform probability model

## Making Inferences and Justifying Conclusions

- Understand and evaluate random processes underlying statistical experiments
- Make inferences and justify conclusions from sample surveys, experiments, and observational studies

## Using Probability to Make Decisions

- Calculate expected values and use them to solve problems
- Use probability to evaluate outcomes of decisions

## Data Analysis and Probability

- Develop and evaluate inferences and predictions that are based on data
- Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them
- Understand and apply basic concepts of probability

## Grades 9-12

Number and operations, measurement, geometry, data analysis and probability, algebra.

- COMPETENCY GOAL 4: The learner will understand and determine probabilities.

## Advanced Functions and Modeling

- Competency Goal 1: The learner will analyze data and apply probability concepts to solve problems.

## Integrated Mathematics

- Competency Goal 3: The learner will analyze data and apply probability concepts to solve problems.

## AP Statistics

- Competency Goal 3: The learner will collect and analyze data to solve problems.

## Number and Operations

- Competency Goal 1: The learner will analyze univariate data to solve problems.
- The student will demonstrate through the mathematical processes an understanding of the relationships between two populations or samples.
- The student will demonstrate through the mathematical processes an understanding of the relationships between two variables within one population or sample.

## Data Analysis & Probability

- The student will understand and apply basic statistical and probability concepts in order to organize and analyze data and to make predictions and conjectures.

## Probability and Statistics

- 9. The student uses experimental and theoretical probability to make predictions.
- 11. The student applies concepts of theoretical and experimental probability to make predictions.
- 7.14 The student will investigate and describe the difference between the probability of an event found through simulation versus the theoretical probability of that same event.

## Textbooks Aligned

How likely is it.

- Investigation One: A First Look at Chance
- Investigation Two: More Experiments with Chance
- Investigation Three: Using Spinners to Predict Chance

## Grade Seven

What do you expect.

- Investigation One: Evaluating Games of Chance
- Investigation Two: Analyzing Number-Cube Games
- Investigation Four: Analyzing Two-Stage Games

## Module 4 - Mind Games

- Section 1: Experimental Probability
- Section 1: Theoretical Probability

## Module 1 - Making Choices

- Section 3: Chance
- Section 3: Theoretical Probability

## Module 2 - At the Mall

- Section 3: Theoretical Probability, Experimental Probability
- Section 3: Tree Diagrams

## Module 4 - Patterns and Discoveries

- Section 6: Triangle Side Length Relationships
- Section 6: Pythagorean Theorem
- Section 6: Geometric Probability

## Module 2 - Bright Ideas

- Section 5: Probability
- Section 3: Exploring Probability

## What Does the Data Say?

- Lesson 10: What Are the Chances?
- Lesson 11: Changing the Chances
- Lesson 12: Which Bag Is Which?

## Chance Encounters

- Lesson 3: From Never to Always
- Lesson 4: Spin with the Cover-Up Game
- Lesson 11: The Shape Toss Game

## Looking Behind the Numbers

- Lesson 9: On Tour

## Great Expectations

- Variability
- Sample Size
- Probability
- Simulations

## Taking A Chance

- Estimating and Computing Chance

## Statistics and the Environment

- Graphs and Tables

## Be Prepared to

- answer the question "Why does my experimental probability not equal my theoretical probability?"
- discuss the difference between experimental and theoretical probablity
- discuss how to determine the experimental probability
- Lesson on Conditional Probability and Probability of Simultaneous Events
- Lesson on Ideas that Lead to Probability

Number Sense

Understanding numbers, their relationships and numerical reasoning

Using symbols to solve equations and express patterns

Studying shapes, sizes and spatial relationships in mathematics

Measurement

Quantifying and comparing attributes like length, weight and volume

Performing mathematical operations like addition, subtraction, division

Probability and Statistics

Analyzing uncertainty and likelihood of events and outcomes

Calculator Suite

Exploring functions, solving equations, constructing geometric shapes

Graphing Calculator

Visualizing equations and functions with interactive graphs and plots

Exploring geometric concepts and constructions in a dynamic environment

3D Calculator

Graphing functions and performing calculations in 3D

Scientific Calculator

Performing calculations with fractions, statistics and exponential functions

Exploring apps bundle including free tools for geometry, spreadsheet and CAS

## Probability

Learn and practice finding event probabilities with interactive resources from GeoGebra.

## Middle School

Certain, likely, unlikely, impossible events.

Indicate the probability of a chance event with or without models as certain, impossible, more likely, less likely, or neither likely nor unlikely using benchmark probabilities of 0, 1/2, and 1.

Exploration

## Spinning Likelihood

Complement of an event.

Determine the complement of an event.

## Determining the Complement of a Spinner Event

Counting strategies for sample spaces.

Determine the sample space for an event using counting strategies (include tree diagrams, permutations, combinations, and the fundamental counting principle).

## Determining the Sample Space of an Event by Building Furry Friends

Frequency tables, line plots and bar graphs.

Interpret probability models for data from simulations or for experimental data presented in tables and graphs (frequency tables, line plots, bar graphs).

## Exploring Cookie Taste Test Probabilities

## Finding Cookie Taste Test Probabilities

## Frequency in Probability Models for Cookie Ingredients

Probabilities in geometry.

Determine a simple probability using geometric figures.

## Calculating Probability Using a Pinball Simulation

Probability of an event as fractions or ratios.

Describe the probability of a chance event using a fraction or ratio.

## Finding Probabilities: Spinner

## Finding Probabilities: Jar of Marbles

Probability of compound events.

Determine the probability of compound events (with and without replacement).

## Possible Probability Outcomes With and Without Replacement

## Probabilities With and Without Replacement

## Calculating Compound Probabilities

Simulations to estimate probabilities of compound events.

Determine a simulation, such as random numbers, spinners, and coin tosses, to model frequencies for compound events.

## Probability Estimation Using Simulation

Theoretical vs. experimental probability.

Determine the probability from experimental results or compare theoretical probabilities and experimental results.

## Finding Theoretical and Experimental Probabilities Using a Spinner Simulation

Using theoretical and experimental probability to make predictions.

Make predictions based on theoretical probabilities or experimental results.

## Predicting Outcomes Using Theoretical Probability

Related topics.

Linear Regression

Statistical Characteristics

## Community Resources

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## Share Suggestion

Experimental vs. theoretical probability: the crazy choices game, web-based practice.

## Grade Levels

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## Virtual Manipulative

Description.

Experimental probability is defined as the chances of something happening, based on repeated testing and observing results. It is the ratio of the number of times an event occurred to the number of times tested. For example, to find the experimental probability of winning a game, one must play the game many times, then divide the number of games won by the total number of games played.

Theoretical probability is defined as the chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four rolls would be a 4.

Specifically, this activity can be used to:

- introduce the concepts of chance and probability
- illustrate the difference between experimental and theoretical probability
- introduce the concept of random numbers

Students can use the Exploration Questions and the Tally Table to guide their investigations.

## Content Collections

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## Theoretical vs. Experimental Probability: How do they differ?

Probability is the study of chances and is an important topic in mathematics. There are two types of probability: theoretical and experimental.

So, how to define theoretical and experimental probability? Theoretical probability is calculated using mathematical formulas, while experimental probability is based on results from experiments or surveys. In order words, theoretical probability represents how likely an event is to happen. On the other hand, experimental probability illustrates how frequently an event occurs in an experiment.

Read on to find out the differences between theoretical and experimental probability. If you wonder How to Understand Statistics Easily , I wrote a whole article where I share 9 helpful tips to help you Ace statistics.

Table of Contents

## What Is Theoretical Probability?

Theoretical probability is calculated using mathematical formulas. In other words, a theoretical probability is a probability that is determined based on reasoning. It does not require any experiments to be conducted. Theoretical probability can be used to calculate the likelihood of an event occurring before it happens.

Keep in mind that theoretical probability doesn’t involve any experiments or surveys; instead, it relies on known information to calculate the chances of something happening.

For example, if you wanted to calculate the probability of flipping a coin and getting tails, you would use the formula for theoretical probability. You know that there are two possible outcomes—heads or tails—and that each outcome is equally likely, so you would calculate the probability as follows: 1/2, or 50%.

## How Do You Calculate Theoretical Probability?

- First, start by counting the number of possible outcomes of the event.
- Second, count the number of desirable (favorable) outcomes of the event.
- Third, divide the number of desirable (favorable) outcomes by the number of possible outcomes.
- Finally, express this probability as a decimal or percentage.

The theoretical probability formula is defined as follows: Theoretical Probability = Number of favorable (desirable) outcomes divided by the Number of possible outcomes.

## How Is Theoretical Probability Used in Real Life?

Probability plays a vital role in the day to day life. Here is how theoretical probability is used in real life:

- Sports and gaming strategies
- Analyzing political strategies.
- Buying or selling insurance
- Determining blood groups
- Online shopping
- Weather forecast
- Online games

## What Is Experimental Probability?

Experimental probability, on the other hand, is based on results from experiments or surveys. It is the ratio of the number of successful trials divided by the total number of trials conducted. Experimental probability can be used to calculate the likelihood of an event occurring after it happens.

For example, if you flipped a coin 20 times and got heads eight times, the experimental probability of obtaining heads would be 8/20, which is the same as 2/5, 0.4, or 40%.

## How Do You Calculate Experimental Probability?

The formula for the experimental probability is as follows: Probability of an Event P(E) = Number of times an event happens divided by the Total Number of trials .

If you are interested in learning how to calculate experimental probability, I encourage you to watch the video below.

## How Is Experimental Probability Used in Real Life?

Knowing experimental probability in real life provides powerful insights into probability’s nature. Here are a few examples of how experimental probability is used in real life:

- Rolling dice
- Selecting playing cards from a deck
- Drawing marbles from a hat
- Tossing coins

The main difference between theoretical and experimental probability is that theoretical probability expresses how likely an event is to occur, while experimental probability characterizes how frequently an event occurs in an experiment.

In general, the theoretical probability is more reliable than experimental because it doesn’t rely on a limited sample size; however, experimental probability can still give you a good idea of the chances of something happening.

The reason is that the theoretical probability of an event will invariably be the same, whereas the experimental probability is typically affected by chance; therefore, it can be different for different experiments.

Also, generally, the more trials you carry out, the more times you flip a coin, and the closer the experimental probability is likely to be to its theoretical probability.

Also, note that theoretical probability is calculated using mathematical formulas, while experimental probability is found by conducting experiments.

## What to read next:

- Types of Statistics in Mathematics And Their Applications .
- Is Statistics Harder Than Algebra? (Let’s find out!)
- Should You Take Statistics or Calculus in High School?
- Is Statistics Hard in High School? (Yes, here’s why!)

## Wrapping Up

Theoretical and experimental probabilities are two ways of calculating the likelihood of an event occurring. Theoretical probability uses mathematical formulas, while experimental probability uses data from experiments. Both types of probability are useful in different situations.

I believe that both theoretical and experimental probabilities are important in mathematics. Theoretical probability uses mathematical formulas to calculate chances, while experimental probability relies on results from experiments or surveys.

I am Altiné. I am the guy behind mathodics.com. When I am not teaching math, you can find me reading, running, biking, or doing anything that allows me to enjoy nature's beauty. I hope you find what you are looking for while visiting mathodics.com.

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IB Maths Vs. A-Level Maths - Which One is Harder?

Maths is a subject that can be demanding for many students. It not only requires strong analytical skills but also an ability to handle complex concepts with ease. Students looking to further their...

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Answer: The theoretical probability is 1/6. The experimental probability is 1/5. Jamal performed an experiment flipping a coin. He did 10 trials and then his arm got tired. He recorded his results in the table. Based on the experimental probability, Jamal predicted that the number of times the coin lands heads up will always be greater than the ...

I love using the Blocko game to give students much needed practice with experimental and theoretical probability. This game also goes by the name "Beano.". I prefer to play it with linking cubes, so we call it Blocko. Algebra 1 is in the midst of our LAST unit of the year. With the stress and craziness that comes with testing + end of year ...

Experimental probability vs theoretical probability. You can see that the relative frequencies are not equal to the theoretical probabilities you would expect if the spinner was fair. If the spinner is fair, the more times an experiment is done, the closer the relative frequencies should be to the theoretical probabilities.

1 Probability Games for the Middle School or High School Classroom. 1.1 Blocko. 1.2 Probability Bingo. 1.3 Greedy Pig Dice Game. 1.4 Teaching Probability with Deal or No Deal. 1.5 Left Center Right Game. 2 Probability Exploration Activities. 2.1 Mystery Box Probability Activity. 2.2 Hex Nut Probability Activity.

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Experimental versus theoretical probability simulation. Theoretical and experimental probability: Coin flips and die rolls. Random number list to run experiment. Random numbers for experimental probability. Interpret results of simulations. Math > AP®︎/College Statistics > Probability >

Trial - A trial is a single, pre-defined test. Experiment - An experiment is a repetition of a trial multiple times in order to observe how often each outcome occurs. Probability - The probability that an event will occur is the proportion of times the event is expected to happen in a suitably large experiment. Licence.

This activity allows the user to conduct probability experiments with traditional probability devices such as a spinner and dice. Studying random events with such devices and computer simulations allows you to gain familiarity with the connection between experimental and theoretical probability. The study of probability allows mathematicians ...

Create a free account so you can save your progress any time and access thousands of math resources for you to customize and share with others. Discover 15 free and ready-to-use GeoGebra resources to explore and practice probability for grades 4-8. Learn how to find probabilities from experiments, sample spaces, and compound events.

Theoretical probability is defined as the chances of events happening as determined by calculating results that would occur under ideal circumstances. For example, the theoretical probability of rolling a 4 on a four-sided die is 1/4 or 25%, because there is one chance in four to roll a 4, and under ideal circumstances one out of every four ...

How the results of the experimental probability may approach the theoretical probability? Example: The spinner below shows 10 equally sized slices. Heather spun 50 times and got the following results. a) From Heather's' results, compute the experimental probability of landing on yellow.

Theoretical and experimental probabilities are two ways of calculating the likelihood of an event occurring. Theoretical probability uses mathematical formulas, while experimental probability uses data from experiments. Both types of probability are useful in different situations. I believe that both theoretical and experimental probabilities ...

Experimental and Theoretical Probability This video defines and uses both experimental and theoretical probabilities. Example: 1. A player hit the bull's eye on a circular dart board 8 times out of 50. Find the experimental probability that the player hits a bull's eye. 2. Find the theoretical probability of rolling a multiple of 3 with a ...

Experimental Probability: Experiment with probability using a fixed size section spinner, a variable section spinner, two regular 6-sided dice or customized dice. On a mission to transform learning through computational thinking, Shodor is dedicated to the reform and improvement of mathematics and science education through student enrichment ...

Theoretical probability is the expected likelihood of an outcome. Develop a theoretical probability model that gives equally likely outcomes for success. Identify the probability of events based on a uniform sample space. A preview of each game in the learning objective is found below. You can access all of the games on Legends of Learning for ...

THEORETICAL AND EXPERIMENTAL PROBABILITY | Dr Austin Maths. Theoretical Probability with Dice Practice Grid (Editable Word | PDF | Answers) Theoretical Probability with Spinners Practice Grid (Editable Word | PDF | Answers) Theoretical Probability with Counters Practice Grid (Editable Word | PDF | Answers) Theoretical Probability with Playing ...

This video will explain the difference between experimental and theoretical probability as well as teach you how to figure out the probabilities for each one.

Now the experimental probability of landing on heads is The probability is still slightly higher than expected, but as more trials were conducted, the experimental probability became closer to the theoretical probability. Examples: 1. Use the table below to determine the probability of each number on a number cube. Let's Review:

Theoretical vs Experimental Probabilities. In the study of probability, there are two main methods of determining the likelihood of an event occurring: theoretical probability and experimental probability. These two approaches provide different perspectives on probability and are used in different scenarios. 1. Theoretical Probability

Experimental and Theoretical Probability This video defines and uses both experimental and theoretical probabilities. Examples: A player hits the bull's eye on a circular dart board 8 times out of 50. Find the experimental probability that the player hits the bull's eye. Find the theoretical probability of rolling a multiple of 3 with a ...

Theoretical probability is based on reasoning and mathematics. Experimental probability is based on the results of several trials or experiments. Theoretical probability is calculated by taking ...

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Theoretical probability is most useful for forming a hypothesis about what will happen. Experimental probability, on the other hand, is most useful for saying what did happen. This in turn can be used to state whether the hypothesis was accurate or not, and help us to work out the likelihood of something happening in the future.