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Experimental Mathematics

Experimental mathematics is a type of mathematical investigation in which computation is used to investigate mathematical structures and identify their fundamental properties and patterns. As in experimental science, experimental mathematics can be used to make mathematical predictions which can then be verified or falsified on the bases of additional computational experiments.

Borwein and Bailey (2003, pp. 2-3) use the term "experimental mathematics" to mean the methodology of doing mathematics that includes the use of computation for:

1. Gaining insight and intuition.

2. Discovering new patterns and relationships.

3. Using graphical displays to suggest underlying mathematical principles.

4. Testing and especially falsifying conjectures.

5. Exploring a possible result to see if it is worth formal proof.

6. Suggesting approaches for a formal proof.

7. Replacing lengthy hand derivations with computer-based derivations.

8. Confirming analytically derived results.

Examples of tools of experimental mathematics include computer algebra , symbolic algebra , Gröbner basis , integer relation algorithms (such as the LLL algorithm and PSLQ algorithm ), arbitrary precision numerical evaluations, computer visualization, cellular automata and related structures, and databases of mathematical structures such as the Online Encyclopedia of Integer Sequences ( http://www.research.att.com/~njas/sequences ) by Neil Sloane, The Wolfram Functions Site ( http://functions.wolfram.com ) by Michael Trott and Oleg Marichev, and MathWorld ( http://mathworld.wolfram.com ) by Eric Weisstein.

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Weisstein, Eric W. "Experimental Mathematics." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ExperimentalMathematics.html

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Experimental mathematics

The advent of powerful computers enables mathematicians to look for patterns, correspondences, in fact, make up conjectures which have been verified in several computable cases. This activity is often referred to as "experimental mathematics" . By its very nature, this activity cannot be reported on in the rigorous theorem-proof style of exposition which is standard in mathematics. For this reason, experimental mathematics has created some interest groups of its own, e.g., around the Journal "Experimental Mathematics" , and in mathematical programming .

Yet, the possibility of performing more and more advanced computations by means of little human (programming) effort also had its effect on the standard mathematical rigour of exposition: nowadays conjectures are verified to rather a significantly high degree of computational complexity before being brought forward as such. See [a3] , [a1] for more applied examples.

Two examples in pure mathematics are the " Moonshine conjectures " , where modular functions are related to representations of sporadic finite simple groups (cf. [a2] ), and the "GUE hypothesis" , where joint distributions of zeros of the Riemann zeta-function are equated to those of the eigenvalues of matrices from GUE, the Gaussian unitary ensemble of large-dimensional random Hermitian matrices (cf. [a4] ).

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Experimental Probability

Experimental probability: introduction, experimental probability: definition, experimental probability formula, solved examples, practice problems, frequently asked questions.

In mathematics, probability refers to the chance of occurrence of a specific event. Probability can be measured on a scale from 0 to 1. The probability is 0 for an impossible event. The probability is 1 if the occurrence of the event is certain.

There are two approaches to study probability: experimental and theoretical. 

Suppose you and your friend toss a coin to decide who gets the first turn to ride a new bicycle. You choose “heads” and your friend chooses “tails.” 

Can you guess who will win? No! You have $\frac{1}{2}$ a chance of winning and so does your friend. This is theoretical since you are predicting the outcome based on what is expected to happen and not on the basis of outcomes of an experiment.

So, what is the experimental probability? Experimental probability is calculated by repeating an experiment and observing the outcomes. Let’s understand this a little better.

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Experimental probability, or empirical probability, is the probability calculated by performing actual experiments and gathering or recording the necessary information. How would you define an experiment? The math definition of an experiment is “a process or procedure that can be repeated and that has a set of well-defined possible results or outcomes.”

Consider the same example. Suppose you flip the coin 50 times to see whether you get heads or tails, and you record the outcomes. Suppose you get heads 20 times and tails 30 times. Then the probability calculated using these outcomes is experimental probability. Here, t he experimental meaning is connected with such experiments used to determine the probability of an event.

Now that you know the meaning of experimental probability, let’s understand its formula.

Experimental Probability for an Event A can be calculated as follows:

P(E) $= \frac{Number of occurance of the event A}{Total number of trials}$

Let’s understand this with the help of the last example. 

A coin is flipped a total of 50 times. Heads appeared 20 times. Now, what is the experimental probability of getting heads?

E xperimental probability of getting heads $= \frac{Number of occurrences}{Total number of trials}$

P (Heads) $= \frac{20}{50} = \frac{2}{5}$

P (Tails) $= \frac{30}{50} = \frac{3}{5}$

Experimental Probability vs. Theoretical Probability

Theoretical probability expresses what is expected. On the other hand, experimental probability explains how frequently an event occurred in an experiment.

If you roll a die, the theoretical probability of getting any particular number, say 3, is $\frac{1}{6}$. 

However, if you roll the die 100 times and record how many times 3 appears on top, say 65 times, then the experimental probability of getting 3 is $\frac{65}{100}$.

Theoretical probability for Event A can be calculated as follows:

P(A) $= \frac{Number of outcomes favorable to Event A}{Number of possible outcomes}$

In the example of flipping a coin, the theoretical probability of the occurrence of heads (or tails) on tossing a coin is

P(H) $= \frac{1}{2}$ and  P(T) $= \frac{1}{2}$ (since possible outcomes are $2 -$ head or tail)

Experimental Probability: Examples

Let’s take a look at some of the examples of experimental probability .

Example 1: Ben tried to toss a ping-pong ball in a cup using 10 trials, out of which he succeeded 4 times. 

P(win) $= \frac{Number of success}{Number of trials}$

             $= \frac{4}{10}$

             $= \frac{2}{5}$

Example 2: Two students are playing a game of die. They want to know how many times they land on 2 on the dice if the die is rolled 20 times in a row. 

The experimental probability of rolling a 2 

$= \frac{Number of times 2 appeared}{Number of trials}$

$= \frac{5}{20}$

$= \frac{1}{4}$

1. Probability of an event always lies between 0 and 1.

2. You can also express the probability as a decimal and a percentage.

Experimental probability is a probability that is determined by the results of a series of experiments. Learn more such interesting concepts at SplashLearn .

1. Leo tosses a coin 25 times and observes that the “head” appears 10 times. What is the experimental probability of getting a head?

 P(Head) $= \frac{Number of times heads appeared}{Total number of trials}$

               $= \frac{10}{25}$

               $= \frac{2}{5}$

               $= 0.4$

2. The number of cakes a baker makes per day in a week is given as 7, 8, 6, 10, 2, 8, 3. What is the probability that the baker makes less than 6 cakes the next day?

Solution: 

Number of cakes baked each day in a week $= 7, 8, 6, 10, 2, 8, 3$

Out of 7 days, there were 2 days (highlighted in bold) on which the baker made less than 6 cookies.

P$(< 6 $cookies$) = \frac{2}{7}$

3. The chart below shows the number of times a number was shown on the face of a tossed die. What was the probability of getting a 3 in this experiment?

Number of times 3 showed $= 7$

Number of tosses $= 30$

P(3) $= \frac{7}{30}$

4. John kicked a ball 20 times. He kicked 16 field goals and missed 4 times . What is the experimental probability that John will kick a field goal during the game?

Solution:  

John succeeded in kicking 16 field goals. He attempted to kick a field goal 20 times. 

So, the number of trials $= 20$

John’s experimental probability of kicking a field goal $= \frac{Successful outcomes} {Trials attempted} = \frac{16}{20}$ 

$= \frac{4}{5}$

$= 0.8$ or $80%$

5. James recorded the color of bikes crossing his street. Of the 500 bikes, 10 were custom colors, 100 were white, 50 were red, 120 were black, 100 were silver, 60 were blue, and 60 were gray. What is the probability that the car crossing his street is white?

Number of white bikes $= 100$ 

Total number of bikes $= 500$

P(white bike) $=  \frac{100}{500} = \frac{1}{5}$

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In a class, a student is chosen randomly in five trials to participate in 5 different events. Out of chosen students, 3 were girls and 2 were boys. What is the experimental probability of choosing a boy in the next event?

A manufacturer makes 1000 tablets every month. after inspecting 100 tablets, the manufacturer found that 30 tablets were defective. what is the probability that you will buy a defective tablet, the 3 coins are tossed 1000 times simultaneously and we get three tails $= 160$, two tails $= 260$, one tail $= 320$, no tails $= 260$. what is the probability of occurrence of two tails, the table below shows the colors of shirts sold in a clothing store on a particular day and their respective frequencies. use the table to answer the questions that follow. what is the probability of selling a blue shirt.

Jason leaves for work at the same time each day. Over a period of 327 working days, on his way to work, he had to wait for a train at the railway crossing for 68 days. What is the experimental probability that Jason has to wait for a train on his way to work?

What is the importance of experimental probability?

Experimental probability is widely used in research and experiments in various fields, such as medicine, social sciences, investing, and weather forecasting.

Is experimental probability always accurate?

Predictions based on experimental probability are less reliable than those based on theoretical probability.

Can experimental probability change every time the experiment is performed?

Since the experimental probability is based on the actual results of an experiment, it can change when the results of an experiment change.

What is theoretical probability?

The theoretical probability is calculated by finding the ratio of the number of favorable outcomes to the total number of probable outcomes.

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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%

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• 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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Experimental probability

Experimental probability (EP), also called empirical probability or relative frequency , is probability based on data collected from repeated trials.

Experimental probability formula

Let n represent the total number of trials or the number of times an experiment is done. Let p represent the number of times an event occurred while performing this experiment n times.

Example #1: A manufacturer makes 50,000 cell phones every month. After inspecting 1000 phones, the manufacturer found that 20 phones are defective. What is the probability that you will buy a phone that is defective? Predict how many phones will be defective next month.

The total number of times the experiment is conducted is n = 1000

The number of times an event occurred is p  = 20 

Experimental probability is performed when authorities want to know how the public feels about a matter. Since it is not possible to ask every single person in the country, they may conduct a survey by asking a sample of the entire population. This is called population sampling. Example #2 is an example of this situation.

There are about 319 million people living in the USA. Pretend that a survey of 1 million people revealed that 300,000 people think that all cars should be electric. What is the probability that someone chosen randomly does not like electric car? How many people like electric cars?

Notice that the number of people who do not like electric cars is 1000000 - 300000 = 700000

Difference between experimental probability and theoretical probability

You can argue the same thing using a die, a coin, and a spinner. We will though use a coin and a spinner to help you see the difference.

Using a coin 

In theoretical probability, we say that "each outcome is equally likely " without the actual experiment. For instance, without  flipping a coin, you know that the outcome could either be heads or tails.  If the coin is not altered, we argue that each outcome (heads or tails) is equally likely. In other words, we are saying that in theory or (supposition, conjecture, speculation, assumption, educated guess) the probability to get heads is 50% or the probability to get tails in 50%. Since you did not actually flip the coin, you are making an assumption based on logic.

The logic is that there are 2 possible outcomes and since you are choosing 1 of the 2 outcomes, the probability is 1/2 or 50%. This is theoretical probability or guessing probability or probability based on assumption.

In the example above about flipping a coin, suppose you are looking for the probability to get a head. 

Then, the number of favorable outcomes is 1 and the number of possible outcomes is 2.

In experimental probability,  we want to take the guess work out of the picture, by doing the experiment to see how many times heads or teals will come up. If you flip a coin 1000 times, you might realize that it landed on heads only 400 times. In this case, the probability to get heads is only 40%. 

Your experiment may not even show tails until after the 4th flip and yet in the end you ended up with more tails than heads. 

If you repeat the experiment another day, you may find a completely different result. May be this time the number of heads is 600 and the number of tails is 400.

Using a spinner

Suppose a spinner has four equal-sized sections that are red, green, black, and yellow. 

In theoretical probability, you will not spin the spinner. Instead, you will say that the probability to get green is one-fourth or 25%. Why 25%? The total number of outcomes is 4 and the number of favorable outcomes is 1.

1/4 = 0.25 = 25%

However, in experimental probability, you may decide to spin the spinner 50 times or even more to see how many times you will get each color.

Suppose you spin the spinner 50 times. It is quite possible that you may end up with the result shown below:

Red: 10 Green: 15 Black: 5 Yellow: 20

Now, the probability to get green is 15/50 = 0.3 = 30%

As you can see, experimental probability is based more on facts, data collected, experiment or research!

Theoretical probability

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In probability and statistics, an experiment typically refers to a study in which the experimenter is trying to determine whether there is a relationship between two or more variables. In an experiment, the subjects are randomly assigned to either a treatment group or a control group (there can be more than one of either group).

Generally, the control group in an experiment receives a placebo (substance that has no effect) or no treatment at all. The treatment group receives the experimental treatment. The goal of the experiment is to determine whether or not the treatment has the desired/any effect that differs from the control group to a degree that the difference can be attributed to the treatment rather than to random chance or variability. Well-designed experiments can yield informative and unambiguous conclusions about cause and effect relationships.

As an example, if a scientist wants to test whether a new medication they developed has any effect, they would select subjects from a common population and randomly assign them to either a treatment group or a control group. They would then administer the treatment to the treatment group, and either a placebo or no treatment to the control group, and study the effects of each using statistical measures to determine whether the medication had any effect beyond chance or variability.

Note that an experiment does not necessarily need to have a physical treatment. The term "treatment" is used fairly loosely. Another experiment could look at the effects of getting advice from a college counselor on admission rates compared to not getting advice from a college counselor. In this case, the "treatment" would be getting advice from a college counselor. The control group would get no advice from a college counselor.

Importance of experimental design

Like survey methodology , experimental design is essential to the validity of the results of the experiment. A poorly designed experiment can result in false or incorrect conclusions. Proper statistical experiment design generally involves the following:

• Identification of the explanatory variable, also referred to as the independent variable . The explanatory variable is the "treatment," or the thing that causes the change, and can be anything that causes a change in the response variable.
• Identification of the response variable, also referred to as the dependent variable . It is the variable that may be affected by the explanatory/independent variable.
• Defining the population of interest and taking a random sample from the population. Generally the larger the random sample, the less potential for sample error, since the larger sample will likely be more representative of the population.
• Random assignment of the subjects in the sample to either the treatment group or the control group.
• Administration of the treatment to the treatment group, and placebo (or nothing) to the control group), possibly using a blind experiment (the subject doesn't know whether they are receiving the treatment or the placebo) or double blind experiment (neither experimenter nor subject knows which treatment they are getting).
• Measurement of the response over a chosen period of time.
• Statistical analysis of the supposed response to determine whether there is an actual response, or the response can be attributed to chance, to determine whether there is a causal relationship between the treatment and the response.
• Replication of the experiment by peers, assuming there is a causal relationship between the treatment and the response.

Experiments vs surveys

Experiments and surveys are both techniques used as part of inferential statistics . A survey involves the use of a random sample of the population, rather than the whole, with the goal that all subjects in the population have an equal chance of being selected. The random sample of the population is then used to draw conclusions or make inferences about the population as a whole.

In contrast, an experiment typically involves the use of random assignment such that all subjects have an equal chance of being assigned to the groups (treatment and control) in the study, which minimizes potential biases, as well as allows the experimenters to evaluate the role of variability in the experiment. This in turn allows them to determine whether any observed differences between the groups merit further study or not based on whether or not the differences can be attributed to variability or chance.

Something that can be repeated that has a set of possible results.

Examples: • Rolling dice to see what random numbers come up. • Asking your friends to choose a favorite pet from a list

Experiments help us find out information by collecting data in a careful manner.

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• Experimental Probability

Experimental probability , also known as empirical probability , is a concept in mathematics that deals with estimating the likelihood of an event occurring based on actual experimental results. Unlike theoretical probability , which predicts outcomes based on known possibilities, experimental probability is derived from real-life experiments and observations.

To understand this better, imagine flipping a coin. The theoretical probability of landing heads is 50% or 1/2. However, if you actually flip the coin 100 times and record the outcomes, you might get heads 48 times. The experimental probability of getting heads would then be 48/100 or 0.48.

In this article, we will explore the concept of experimental probability, its significance, and how it differs from theoretical probability. We will discuss the formula for calculating experimental probability, provide examples to illustrate its application.

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What is Probability?

What is experimental probability, formula for experimental probability, examples of experimental probability, what is theoretical probability, experimental probability vs theoretical probability.

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The branch of mathematics that tells us about the likelihood of the occurrence of any event is the probability . Probability tells us about the chances of happening an event.

The probability of any element that is sure to occur is One(1) whereas the probability of any impossible event is Zero(0). The probability of all the elements ranges between 0 to 1.

There are two ways of studying probability that are

• Theoretical Probability

Now let’s learn about both in detail.

Experimental probability is a type of probability that is calculated by conducting an actual experiment or by performing a series of trials to observe the occurrence of an event. It is also known as empirical probability.

To calculate experimental probability, you need to conduct an experiment by repeating the event multiple times and observing the outcomes. Then, you can find the probability of the event occurring by dividing the number of times the event occurred by the total number of trials.

The experimental Probability for Event A can be calculated as follows:

P(E) = (Number of times an event occur in an experiment) / (Total number of Trials)

Now, as we learn the formula, let’s put this formula in our coin-tossing case.  If we tossed a coin 10 times and recorded a head 4 times and a tail 6 times then the Probability of Occurrence of Head on tossing a coin:

P(H) = 4/10

Similarly, the Probability of Occurrence of Tails on tossing a coin:

P(T) = 6/10

Theoretical Probability deals with assumptions in order to avoid unfeasible or expensive repetition experiments. The theoretical Probability for an Event A can be calculated as follows:

P(A) = Number of outcomes favorable to Event A / Number of all possible outcomes            

Now, as we learn the formula, let’s put this formula in our coin-tossing case. In tossing a coin, there are two outcomes: Head or Tail.

Hence, The Probability of occurrence of Head on tossing a coin is

Similarly, The Probability of the occurrence of a Tail on tossing a coin is

There are some key differences between Experimental and Theoretical Probability , some of which are as follows:

• Probability in Maths
• Probability Distribution
• Bayes’ Theorem

Solved Examples of Experimental Probability

Example 1. Let’s take an example of tossing a coin, tossing it 40 times , and recording the observations. By using the formula, we can find the experimental probability for heads and tails as shown in the below table.

Number of Trail Outcome Number of Trail Outcome Number of Trail Outcome Number of Trail Outcome First H Eleventh T Twenty-first T Thirty-first T Second T Twelfth T Twenty-second H Thirty-second H Third T Thirteenth H Twenty-third T Thirty-third T Fourth H Fourteenth H Twenty-fourth H Thirty-fourth H Fifth H Fifteenth H Twenty-fifth T Thirty-fifth T Sixth H Sixteenth H Twenty-sixth H Thirty-sixth T Seventh T Seventeenth T Twenty-seventh T Thirty-seventh T Eighth H Eighteenth T Twenty-eighth T Thirty-eighth H Ninth T Nineteenth T Twenty-ninth T Thirty-ninth T Tenth H Twentieth T Thirtieth H Fortieth T The formula for experimental probability: P(H) = Number of Heads ÷ Total Number of Trials = 16 ÷ 40 = 0.4 Similarly, P(H) = Number of Tails ÷ Total Number of Trials = 24 ÷ 40 = 0.6 P(H) + P(T) = 0.6 + 0.4 = 1 Note: Repeat this experiment for ‘n’ times and then you will find that the number of times increases, the fraction of experimental probability comes closer to 0.5. Thus if we add P(H) and P(T), we will get  0.6 + 0.4 = 1 which means P(H) and P(T) is the only possible outcomes.

Example 2. A manufacturer makes 50,000 cell phones every month. After inspecting 1000 phones, the manufacturer found that 30 phones are defective. What is the probability that you will buy a phone that is defective? Predict how many phones will be defective next month.

Experimental Probability = 30/1000 = 0.03 0.03 = (3/100) × 100 = 3% The probability that you will buy a defective phone is 3% ⇒ Number of defective phones next month = 3% × 50000 ⇒ Number of defective phones next month = 0.03 × 50000 ⇒ Number of defective phones next month = 1500

Example 3. There are about 320 million people living in the USA. Pretend that a survey of 1 million people revealed that 300,000 people think that all cars should be electric. What is the probability that someone chosen randomly does not like the electric car? How many people like electric cars?

Now the number of people who do not like electric cars is 1000000 – 300000 = 700000 Experimental Probability =  700000/1000000 = 0.7 And, 0.7 = (7/10) × 100 = 70% The probability that someone chose randomly does not like the electric car is 70% The probability that someone like electric cars is  300000/1000000 = 0.3 Let x be the number of people who love electric cars ⇒ x = 0.3 × 320 million ⇒ x = 96 million The number of people who love electric cars is 96 million.

Practice Problems on Experimental Probability

Problem 1: A coin is flipped 200 times, and it lands on heads 120 times. What is the experimental probability of getting heads?

Problem 2: A die is rolled 50 times, and the number 3 appears 8 times. What is the experimental probability of rolling a 3?

Problem 3: In a class survey, 150 students were asked if they prefer reading books or watching movies. 90 students said they prefer watching movies. What is the experimental probability that a randomly chosen student prefers watching movies?

Problem 4: A bag contains 5 red, 7 blue, and 8 green marbles. If 40 marbles are drawn at random with replacement, and 12 of them are red, what is the experimental probability of drawing a red marble?

Problem 5: A basketball player made 45 successful free throws out of 60 attempts. What is the experimental probability that the player will make a free throw?

Problem 6: During a game, a spinner is spun 80 times, landing on a specific section 20 times. What is the experimental probability of the spinner landing on that section?

FAQs on Experimental Probability

Define experimental probability..

Probability of an event based on an actual trail in physical world is called experimental probability.

How is Experimental Probability calculated?

Experimental Probability is calculated using the following formula:  P(E) = (Number of trials taken in which event A happened) / Total number of trials

Can Experimental Probability be used to predict future outcomes?

No,  experimental probability can’t be used to predict future outcomes as it only achives the theorectical value when the trails becomes infinity.

How is Experimental Probability different from Theoretical Probability?

 Theoretical probability is the probability of an event based on mathematical calculations and assumptions, whereas experimental probability is based on actual experiments or trials.

What are some Limitations of Experimental Probability?

There are some limitation of experimental probability, which are as follows: Experimental probability can be influenced by various factors, such as the sample size, the selection process, and the conditions of the experiment.  The number of trials conducted may not be sufficient to establish a reliable pattern, and the results may be subject to random variation.  Experimental probability is also limited to the specific conditions of the experiment and may not be applicable in other contexts.

Can Experimental Probability of an event be a negative number if not why?

As experimental probability is given by: P(E) = Number of trials taken in which event A happened/Total number of trials Thus, it can’t be negative as both number are count of something and counting numbers are 1, 2, 3, 4, …. and they are never negative.

What are Types of Probability?

There are two forms of calculating the probability of an event that are, Theoretical Probability Experimental Probability

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Chapter 14: Statistics

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Chapter 15: Probability

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