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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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3.2: Three Types of Probability

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Learning Objectives

• Find theoretical probabilities
• Find empirical probabilities
• Find subjective probabilities

Probability is the likelihood of an event happening. Probabilities can be given as a percent, a decimal or a reduced fraction. The notation for the probability of event A is P( A ). Here are some important characteristics of probabilities:

• The probability of any event A is a number between 0 and 1:

0 ≤ P( A ) ≤ 1

• The sum of the probabilities of all of the outcomes in the sample space is 1:

P( A 1 ) + P( A 2 ) + … + P( A n ) = 1

• P( A ) = 0 means that event A will not happen
• P( A ) = 1 means that event A will definitely happen

There are three types of probability: theoretical, empirical, and subjective.

Classical Approach to Probability (Theoretical Probability)

Formula: theoretical probability.

\[P(A) = \dfrac{\text{Number of ways A can occur}}{\text{Number of different outcomes in S}}\]

The classical approach can only be used if each outcome has equal probability.

Example \(\PageIndex{1}\)

If an experiment consists of flipping a coin twice, compute the probability of getting exactly two heads.

There are 4 outcomes in the samples space, S = {HH, HT, TH, TT}. The event of getting exactly two heads is A = {HH}. The number of ways A can occur is 1. Thus P( A ) = \(\dfrac{1}{4}\).

Example \(\PageIndex{2}\)

If a random experiment consists of rolling a six-sided die, compute the probability of rolling a 4.

The sample space is S = {1, 2, 3, 4, 5, 6}. The event A is that you want is to get a 4, and the event space is A = {4}. Thus, in theory, the probability of rolling a 4 would be P( A ) = \(\dfrac{1}{6}\) = 0.1667.

Example \(\PageIndex{3}\)

Suppose you have an iPhone with the following songs on it: 5 Rolling Stones songs, 7 Beatles songs, 9 Bob Dylan songs, 4 Johnny Cash songs, 2 Carrie Underwood songs, 7 U2 songs, 4 Mariah Carey songs, 7 Bob Marley songs, 6 Bunny Wailer songs, 7 Elton John songs, 5 Led Zeppelin songs, and 4 Dave Matthews Band songs. The different genre that you have are rock from the ‘60s which includes Rolling Stones, Beatles, and Bob Dylan; country which includes Johnny Cash and Carrie Underwood; rock of the ‘90s includes U2 and Mariah Carey; reggae which includes Bob Marley and Bunny Wailer; rock of the ‘70s which includes Elton John and Led Zeppelin; and bluegrass/rock which includes Dave Matthews Band.

• What is the probability that you will hear a Bunny Wailer song?
• What is the probability that you will hear a song from the ‘60s?
• What is the probability that you will hear a reggae song?
• What is the probability that you will hear a song from the ‘90s or a bluegrass/rock song?
• What is the probability that you will hear an Elton John or a Carrie Underwood song?
• What is the probability that you will hear a country song or a U2 song?
• An iPhone in shuffle mode randomly picks the next song so you have no idea what the next song will be. Now you would like to calculate the probability that you will hear the type of music or the artist that you are interested in. The sample set is too difficult to write out, but you can figure it from looking at the number in each set and the total number. The total number of songs you have is 67. There are 4 Johnny Cash songs out of the 67 songs. Thus, P(Johnny Cash song) = \(\dfrac{4}{67}\) = 0.0597
• There are 6 Bunny Wailer songs. Thus, P(Bunny Wailer) = \(\dfrac{6}{67}\) = 0.0896.
• There are 5, 7, and 9 songs that are classified as rock from the ‘60s, which is a total of 21. Thus, P(rock from the ‘60s) = \(\dfrac{21}{67}\) = 0.3134.
• There are total of 13 songs that are classified as reggae. Thus, P(reggae) = \(\dfrac{13}{67}\) = 0.1940.
• There are 7 and 4 songs that are songs from the ‘90s and 4 songs that are bluegrass/rock, for a total of 15. Thus, P(rock from the ‘90s or bluegrass/rock) = \(\dfrac{15}{67}\) = 0.2239.
• There are 7 Elton John songs and 2 Carrie Underwood songs, for a total of 9. Thus, P(Elton John or Carrie Underwood song) =\(\dfrac{9}{67}\) = 0.1343.
• There are 6 country songs and 7 U2 songs, for a total of 13. Thus, P(country or U2 song) = \(\dfrac{13}{67}\) = 0.1940.

Empirical Probability (Experimental or Relative Frequency Probability)

Definition: empirical probability.

The experiment is performed many times and the number of times that event A occurs is recorded. Then the probability is approximated by finding the relative frequency.

\[P(A) = \dfrac{\text{Number of times A occurred}}{\text{Number of times the experiment was repeated}}\]

Example \(\PageIndex{4}\)

Suppose that the experiment is rolling a die. Find the empirical probability of rolling a 4.

The sample space is S = {1, 2, 3, 4, 5, 6}. The event A is that you want is to get a 4, and the event space is A = {4}. To do this, roll a die 10 times and count the number of times you roll a 4. When you do that, you get 4 two times. Based on this experiment, the probability of getting a 4 is 2 out of 10 or \(\dfrac{1}{5}\) = 0.2. To get more accuracy, repeat the experiment more times. It is easiest to put this information in a table, where n represents the number of times the experiment is repeated. When you put the number of 4s rolled divided by the number of times you repeat the experiment, you get the relative frequency. See the last column in Figure \(\PageIndex{1}\).

Figure \(\PageIndex{1}\): Trials for Die Experiment

Notice that as n increased, the relative frequency seems to approach a number; it looks like it is approaching 0.163. You can say that the probability of getting a 4 is approximately 0.163. If you want more accuracy, then increase n even more by rolling the die more times.

These probabilities are called experimental probabilities since they are found by actually doing the experiment or simulation. They come about from the relative frequencies and give an approximation of the true probability.

The approximate probability of an event \(A\), notated as \(P(A)\), is

For the event of getting a 4, the probability would be P(4) = \(\dfrac{163}{1000}\) = 0.163

Definition: Law of Large Numbers

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. Note the x -axis is in a log scale.

Note that the more times you roll the die, the closer the experimental probability gets to the theoretical probability, which illustrates the Law of Large Numbers.

Figure \(\PageIndex{2}\)

You can compute experimental probabilities whenever it is not possible to calculate probabilities using other means. An example is if you want to find the probability that a family has 5 children, you would have to actually look at many families, and count how many have 5 children. Then you could calculate the probability. Another example is if you want to figure out if a die is fair. You would have to roll the die many times and count how often each side comes up. Make sure you repeat an experiment many times, because otherwise you will not be able to estimate the true probability of 5 children or the fairness of the die. This is due to the Law of Large Numbers, since the more times we repeat the experiment, the closer the experimental probabilities will get to the theoretical probabilities. For difficult theoretical probabilities, we can run computer simulations that can do an experiment repeatedly, many times, very quickly and come up with accurate estimates of the theoretical probability.

Example \(\PageIndex{5}\)

A fitness center coach kept track of members over the last year. They recorded if the person stretched before they exercised, and whether they sustained an injury. The following contingency table shows their results. Select one member at random and find the following probabilities.

• Find the probability that a member sustained an injury.
• Find the probability that a member did not stretch.
• Find the probability that a member sustained an injury and did not stretch.
• Find the totals for each row, column, and grand total.

Next, find the relative frequencies by dividing each number by the total of 400.

Using the formula for probability. we get P(Injury) = \(\dfrac{\text{Number of injuries}}{\text{Total number of people}}\) = \(\dfrac{73}{400}\) = 0.1825.

Using the table, we can get the same answer very quickly by just taking the column total under Injury to get 0.1825. As we get more complicated probability questions, these contingency tables will help organize your data.

• Using the relative frequency contingency table, take the total of the row for all the members that did not stretch and we get the P(Did Not Stretch) = 0.195.
• Using the relative frequency contingency table, take the intersection of the injury column with the did not stretch row and we get P(Injury and Did Not Stretch) = 0.0525.

Subjective Probability

Definition: subjective probability.

Subjective probability is the probability of event A estimated using previous knowledge and is someone’s opinion.

Example \(\PageIndex{6}\)

Find the probability of meeting Dolly Parton.

I estimate the probability of meeting Dolly Parton to be \(1.2 \times 10^{-9}\) = 1.2 E-9 \(\approx\) 0.0000000012. This is a very small probability and essentially means that the probability is 0 and meeting Dolly Parton will not happen.

Example \(\PageIndex{7}\)

What is the probability it will rain tomorrow?

A weather reporter looks at several forecasts, uses their expert knowledge of the region, and reports the probability that it will rain tomorrow is 80%.

Theoretical and Experimental Probability

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Theoretical Probability versus Experimental Probability

You've heard the terms, theoretical probability and experimental probability , but what do they mean?

Are they in anyway related? This is what we are going to discover in this lesson.

If you've completed the lessons on i ndependent and dependent probability , then you've already found the theoretical probability for numerous problems.

Theoretical Probability

Theoretical probability is the probability that is calculated using math formulas. This is the probability based on math theory.

Experimental Probability

Experimental probability is calculated when the actual situation or problem is performed as an experiment. In this case, you would perform the experiment, and use the actual results to determine the probability.

In order to accurately perform an experiment, you must:

• Identify what constitutes a " trial ".
• Perform a minimum of 25 trials
• Set up an organizer (table or chart) to record your data.

Let's take a look at an example where we first calculate the theoretical probability, and then perform the experiment to determine the experimental probability.

It will be interesting to compare the theoretical probability and the experimental probability. Do you think the two calculations will be close?

Example 1 - Theoretical Versus Experimental

This problem is from Example 1 in the  independent events  lesson. We calculated the theoretical probability to be 1/12 or 8.3%. Take a look:

Since we know that the theoretical probability is 8.3% chance of flipping a head and rolling a 6, let's see what happens when we actually perform the experiment.

Identify a trial: A trial consists of flipping a coin once and rolling a die once.

Conduct 25 trials and record your data in the table below.

For each trial, I flipped the coin once and rolled the die. I recorded and H for heads and a T for tails in the row labeled "Coin."

I recorded the number on the die in the row labeled "Die".

In the last row I determined whether the trial completed the event of flipping a head and rolling a six.

In this experiment, there was only 1 trial (out of 25) where a head was flipped on the coin and a 6 was rolled on the die.

This means that the experimental probability is 1/25 or 4%.

Please note that everyone's experiment will be different; thus allowing the experimental probability to differ.

Also, the more trials that you conduct in your experiment, the closer your calculations will be for the experimental and theoretical probabilities.

Conclusions

The theoretical probability is 8.3% and the experimental probability is 4%. Although the experimental probability is slightly lower, this is not a significant difference.

In most experiments, the theoretical probability and experimental probability will not be equal; however, they should be relatively close.

If the calculations are not close, then there's a possibility that the experiment was conducted improperly or more trials need to be completed.

I hope this helps to give you a sense of how to set up an experiment in order to compare theoretical versus experimental probabilities.

• Probability
• Theoretical/Experimental Probability

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Theoretical and Experimental Probability

More specific topics in theoretical and experimental probability.

• Simple and Theoretical Probability
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Theoretical Probability: Definition + Examples

Probability is a topic in statistics that describes the likelihood of certain events happening. When we talk about probability, we’re often referring to one of two types:

1. Theoretical probability

Theoretical probability is the likelihood that an event will happen based on pure mathematics. The formula to calculate the theoretical probability of event  A  happening is:

P( A ) = number of desired outcomes / total number of possible outcomes

For example, the theoretical probability that a dice lands on “2” after one roll can be calculated as:

P( land on 2 ) = (only one way the dice can land on 2) / (six possible sides the dice can land on) = 1/6

2. Experimental probability

Experimental probability is the actual probability of an event occurring that you directly observe in an experiment. The formula to calculate the experimental probability of event  A  happening is:

P( A ) = number of times event occurs / total number of trials

For example, suppose we roll a dice 11 times and it lands on a “2” three times. The experimental probability for the dice landing on “2” can be calculated as:

P( land on 2 ) = (lands on 2 three times) / (rolled the dice 11 times) =  3/11

How to Remember the Difference

You can remember the difference between theoretical probability and experimental probability using the following trick:

• The theoretical probability of an event occurring can be calculated in theory using math.
• The experimental probability of an event occurring can be calculated by directly observing the results of an experiment .

The Benefit of Using Theoretical Probability

Statisticians often like to calculate the theoretical probability of events because it’s much easier and faster to calculate compared to actually conducting an experiment.

For example, suppose it’s known that 1 out of every 30 students at a particular school will need additional help with their math homework after school. Instead of waiting to see how many students show up for homework help after school, a school administrator could instead calculate the total number of students at the school (suppose it’s 300) and multiply by the theoretical probability (1/30) to know that he will likely need 10 people present to help each of the students one-on-one.

Examples of Theoretical Probability

Experimental probabilities are usually easier to calculate than theoretical probabilities because it just involves counting the number of times that a certain event actually occurred relative to the total number of trials.

Conversely, theoretical probabilities can be trickier to calculate. So, here are several examples of how to calculate theoretical probabilities to help you master the topic.

A bag contains the following:

• 3 red balls
• 4 green balls
• 2 purple balls

Question: If you close your eyes and randomly pull out one ball, what is the probability that it will be green?

Answer:  We can use the following formula to calculate the theoretical probability of pulling out a green ball:

P( green ) = (4 green balls) / (9 total balls) = 4/9

You own a 9-sided dice that contains the numbers 1 through 9 on the sides.

Question:  What is the probability that the dice lands on “7” if you were to roll it one time?

Answer:  We can use the following formula to calculate the theoretical probability that the dice lands on 7:

P( lands on 7 ) = (only one way the dice can land on 7) / (9 possible sides) =  1/9

A bag contains the name of 3 boys and 7 seven girls.

Question:  If you close your eyes and randomly pull one name out of the bag, what is the probability that you pull out a girl’s name?

Answer:  We can use the following formula to calculate the theoretical probability that you pull out a girl’s name:

P( girls name ) = (7 possible girl names) / (10 total names) =  7/10

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Theoretical and experimental probability

There are two different types of probability that we often talk about: theoretical probability and experimental probability.

Theoretical probability describes how likely an event is to occur. We know that a coin is equally likely to land heads or tails, so the theoretical probability of getting heads is 1/2.

Experimental probability describes how frequently an event actually occurred in an experiment. So if you tossed a coin 20 times and got heads 8 times, the experimental probability of getting heads would be 8/20, which is the same as 2/5, or 0.4, or 40%.

The theoretical probability of an event will always be the same, but the experimental probability is affected by chance, so it can be different for different experiments. The more trials you carry out (for example, the more times you toss the coin), the closer the experimental probability is likely to be to the theoretical probability.

Maybe you could try tossing a coin 20 times to see how close your experimental probability is to the theoretical probability.

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Experimental and Theoretical Probability

Probability is a branch of math that studies the chance or likelihood of an event occurring. There are two types of prob ability for a particular event: experimental probability and theoretical probability. Learn the difference between the two types of probabilities and the steps involved in their calculation. ...Read More Read Less

Experimental and Theoretical Probability in Math

What is Probability?

• Experimental Probability
• Theoretical Probability
• Solved Examples
• Frequently Asked Questions

Th e chance of a happening is named as the probability of the event happening. It tells us how likely an occasion is going to happen; it doesn’t tell us what’s happening. There is a fair chance of it happening (happening/not happening). They’ll be written as decimals or fractions . The probability of occurrence A is below.

P (A) = \(\frac{\text{Number of favorable outcomes}}{\text{Number of total possible outcomes}}\)

Following are two varieties of probability:

• Experimental probability
• Theoretical probability

What is Experimental Probability

Definition : Probability that’s supported by repeated trials of an experiment is named as experimental probability.

P (event) = \(\frac{\text{Number of times that event occurs}}{\text{Total number of trails}}\)

Example: The table shows the results of spinning a penny 62 times. What’s the probability of spinning heads?

Solution: Heads were spun 23 times in a total of 23 + 39 = 62 spins.

P (heads) = \(\frac{\text{23}}{\text{69}}\) = 0.37  or 37.09 %

What is Theoretical Probability

Definition : When all possible outcomes are equally likely the theoretical possibility of an incident is that the quotient of the number of favorable outcomes and therefore the number of possible outcomes.

P (event) = \(\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\)

Example: You randomly choose one among the letters shown. What’s the theoretical probability of randomly choosing an X?

Solution: P (x) = \(\frac{\text{Number of favorable outcomes}}{\text{Number of possible outcomes}}\) = \(\frac{\text{1}}{\text{7}}\) or 14.28%

A prediction could be a reasonable guess about what is going to happen in the future. Good predictions should be supported by facts and probability.

Predictions supported theoretical probability. These are the foremost reliable varieties of predictions, based on physical relationships that are easy to work and measure which don’t change over time. They include such things as:

• number cubes

Let’s take a look at some differences between experimental and theoretical probability:

Theoretical & Experimental Probability Examples

1. What is the probability of tossing a variety cube and having it come up as a two or a three?

Solution:  

First, find the full number of outcomes

Outcomes: 1, 2, 3, 4, 5, and 6

Total outcomes = 6

Next, find the quantity of favorable outcomes.

Favorable outcomes:

Getting a 2 or a 3 = 2 favorable outcomes

Then, find the ratio of favorable outcomes to total outcomes.

P (Event) = Number of favorable outcomes : total number of outcomes

P (2 or 3) = 2:6

P (2 or 3) = 1:3

The solution is 1:3

The theoretical probability of rolling a 2 or a 3 on a variety of cube is 1:3.

2 . A bag contains 25 marbles. You randomly draw a marble from the bag, record its color, so replace it. The table shows the results after 11 draws. Predict the amount of red marbles within the bag.

To seek out the experimental probability of drawing a red marble.

P (EVENT) = \(\frac{\text{Number of times the event occurs}}{\text{Total number of trials}}\)

P (RED) = \(\frac{\text{5}}{\text{11}}\)        (You draw red 5 times. You draw a complete of 11 marbles)

To make a prediction, multiply the probability of drawing red by the overall number of marbles within the bag.

\(\frac{\text{5}}{\text{11}}\) x 25 = 11.36 ~ 11 so you’ll be able to predict that there are 11 red balls in an exceedingly bag

3. A spinner was spun 1000 times and the frequency of outcomes was recorded as in the given table.

Find (a) list the possible outcomes that you can see in the spinner (b) compare the probability of each outcome (c) find the ratio of each outcome to the total number of times that the spinner spun.

(a) T he possible outcomes are 5. They are red, orange, purple, yellow, and green. Here all the five colors occupy the same area in the spinner. They are all equally likely.

(b) Compute the probability of each event.

P (Red) = \(\frac{\text{Favorable outcomes of red}}{\text{Total number of possible outcomes}}\) = \(\frac{\text{1}}{\text{5}}\) = 0.2

Similarly, P (Orange), P (Purple), P (Yellow) and P (Green) are also \(\frac{\text{1}}{\text{5}}\) or 0.2.

(c) From the experiment the frequency was recorded in the table.

Ratio for red = \(\frac{\text{Number of outcomes of red in the above experiment}}{\text{Number of times the spinner was spun}}\) = \(\frac{\text{185}}{\text{1000}}\) = 0.185

Similarly, we can find the corresponding ratios for orange, purple, yellow, and green are 0.195, 0.210, 0.206, and 0.204 respectively. Can you see that each of the ratios is approximately equal to the probability which we have obtained in (b) [i.e. before conducting the experiment]

How do you find experimental probability?

The experimental probability of an occurrence is predicted by actual experiments and therefore the recordings of the events. It’s adequate to the amount of times an incident occurred divided by the overall number of trials.

How does one find theoretical probability?

When all possible events or outcomes are equally likely to occur, the theoretical probability is found without collecting data from an experiment.

What is experimental probability used for?

Experimental probability, also called Empirical probability, relies on actual experiments and adequate recordings of the happening of events. To work out the occurrence of any event, a series of actual experiments are conducted.

Why is experimental probability different from theoretical?

Theoretical probability describes how likely an occurrence is to occur. We all know that a coin is equally likely to land heads or tails, therefore the theoretical probability of getting heads is 1/2. Experimental probability describes how frequently a happening actually occurred in an experiment.

Is flipping a coin theoretical or experimental probability?

So the results of flipping a coin should be somewhere around 50% heads and 50% tails since that’s the theoretical probability.

Can the experimental probability of an incident be a negative number?

No, since the quantity of trials during which the event can happen can not be negative and also the total number of trials is usually positive.

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Theoretical vs. Experimental Probability Interactive Activity Worksheet

Description

Dive into the world of probability with this interactive worksheet designed to help students master the concepts of theoretical and experimental probability using a simple yet effective coin-flipping experiment. Perfect for classrooms, homeschool settings, or individual practice, this worksheet provides an invaluable hands-on learning experience. This worksheet is designed to make learning probability engaging and effective, ensuring that students not only understand but also enjoy the process of discovering mathematical concepts.

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• Unit 1 - Numbers and Their Opposites
• Unit 2 - Rational Numbers
• Unit 3 - Expressions and Equations
• Unit 4 - Proportional Relationships
• Unit 5 - Probability
• Unit 6a - Geometry (2D Shapes)
• Unit 6b - Geometry (3D Shapes)
• Unit 6c - Geometry (Angles and Triangles)
• Unit 7 - Inferences

Unit 5 - Probability 

Experimental vs. Theoretical Probability

Compound Probability

Study Guide