Experimental vs Theoretical Probability: Difference and Comparison

An experiment can have several possibilities while listing many circumstances, although there are two types of probabilities – Experimental and Theoretical Probability. The term probability is a common term in maths.

Probability lists out events to observe what is likely to happen in an experiment without or after performing an experiment. In other words, it is the prospect of an event happening. 

Key Takeaways

  1. Experimental probability is based on the observed outcomes of an experiment, while theoretical probability relies on mathematical analysis.
  2. Experimental probability can change with each trial, whereas theoretical probability remains constant.
  3. Theoretical probability assumes a fair and unbiased sample space, while experimental probability depends on an experiment’s specific conditions and results.

Experimental vs Theoretical Probability

Experimental probability is a probably based on possible outcomes arrived after gathering information through experiments. The result of the experiment gives the chances of an event happening. Theoretical probability is the possibility of an event happening without an experiment, so it is assumption-based.

Experimental vs Theoretical Probability
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Experimental probability is a probability based on possible outcomes after gathering information by experimenting. In other words, the chances of happening an event by gathering information or collecting data by experimenting.

Its foundation is on what happened during an event. And the formula is the ratio of possible outcomes of a specific event to the total number of trials. 

Theoretical probability is the possibility of an event happening without experimenting. Also, its foundation is assumption-based. In this probability, the experiment does not follow.

However, assumptions are taken into consideration to find a certain probability of an event. And the formula is the ratio of the number of suitable outcomes to the number of plausible outcomes.

Comparison Table

Parameters of comparisonExperimental Probability Theoretical Probability 
DefinitionThe possibility of a specific event happening with actually performing an experiment is experimental probability.The possibility of a specific event based on an assumption without performing an experiment is theoretical probability.
Experiment In experimental probability, an experiment does occur.In theoretical probability, an experiment does not occur. 
Data In experimental probability, the data is collected by experimenting repeatedly.In theoretical probability, the data is collected by considering every possible outcome that has a chance to happen during an experiment without actually performing it. 
Basis of probabilityThe probability in experimental probability is based on facts and data.The probability in theoretical probability is based on assumption.
Consideration of outcomes The experimental probability considers outcomes gathered through experimenting. Theoretical probability considers outcomes that are likely to happen. 
Approach In experimental probability, its approach is based on what has happened.In the theoretical experiment, its approach is based on what would happen considered possible outcomes.
ReliabilityExperimental probability is reliable in batting averages, shooting percentages, and other similar data from sports; predicting the weather, sales figure of a movie or series; polls and surveys that collect opinions; and historical data.Theoretical probability is reliable based on a physical relationship, where objects involved can be seen easily, are measurable, and don’t change over time.
Formula The formula of experimental probability is the ratio of possible outcomes of a specific event to the total number of trials.The formula of theoretical probability is the ratio of the number of suitable outcomes to the number of plausible outcomes. 

What is Experimental Probability? 

Experimental Probability is the probability of the occurrence of a specific event based on an experiment.  It is also known as empirical probability. 

Experimental probability is based on outcomes gathered by repeatedly experimenting. Moreover, it focuses on what happened during an experiment rather than what would happen. 

Some specific outcomes are gathered before determining a certain event’s probability. Besides, an experiment is conducted repeatedly to collect desired outcomes.

Its basic approach differs from theoretical probability, although both find probability. 

Probability based on data and experiment results is reliable as it’s more likely to happen than assumption-based probability.

However, both have their pros and cons. A probability is just a prediction of what is likely to happen in the future. So, it may result in an unexpected outcome. 

Although, an experimental-based probability is more likely to happen due to the greater number of outcomes that lead closer to happening an event.

As we already know, that experimental probability is more reliable.

But, many factors affect the results of an event in many situations, such as batting averages, shooting percentage, and other similar data from sports; predicting the weather, sales figure of a movie or series; polls and surveys that collect opinions; and historical data. 

Coming to the formula the formula of experimental probability is the ratio of possible outcomes of a specific event to the total number of trials. 

What is Theoretical Probability?

Theoretical Probability is the probability of the possibility of a specific event based on an assumption without actually experimenting. It is the theory behind probability. 

For theoretical probability, knowing about an event is necessary rather than experimenting. The chances of happening a specific event are considered rather than actual outcomes.

Moreover, it predicts what will happen in the future based on the possibility of an event. 

It accounts for favourable outcomes for further prediction of the possibility of an event. Rather than relying on data and experiment results, it depends on assumed data.  The approaches of both probabilities are different from each other. 

Its approach is to predict the outcomes without actually performing an event. 

Moreover, it is not considered as reliable as an experimental probability because it does not acknowledge facts and perform an experiment. Although, both probabilities can be proven wrong as other factors affect situations and change the result at last. 

However, it is considered reliable in certain situations, such as a physical relationship based on theoretical probability where the object involved in an event can be seen, measurable, and does not change over time.

It includes coin flippers, spinners, several coins, etc.  

Lastly, the fourth formula is the ratio of the number of suitable outcomes to the number of plausible outcomes.

Main Differences Between Experimental and Theoretical Probability

Probability is the chance of an event happening with or without experimenting. Its ideal approach is to predict what will happen in the future. But, seldom do certain factors affect an event, and the result of an experiment can change drastically.  

There are two types of probabilities – Experimental and Theoretical probability. Both are reliable, yet in different circumstances. 

  1. Experimental probability is the possibility of a particular event happening with experimenting. Meanwhile, the theoretical probability is the possibility of a particular 
  2. In experimental probability, an experiment is performed. While the theoretical probability, an experiment does not.
  3. In experimental probability, the data is gathered by experimenting repeatedly. While in theoretical probability, the data is collected by considering every possible outcome that has a chance to happen during an experiment without actually performing it. 
  4. In experimental probability, outcomes gathered through the experiment are considered for finding the possibility of an event. Meanwhile, theoretical probability considers outcomes that are likely to happen. 
  5. In experimental probability, its approach is based on what has happened, while, in the theoretical experiment, its approach is based on what would happen considered possible outcomes.
  6. Experimental probability is reliable in batting averages, shooting percentages, and other similar data from sports; predicting the weather, sales figure of a movie or series; polls and surveys that collect opinions; and historical data. While the theoretical probability is reliable in a kind of probability based on a physical relationship where objects involved can be seen, measurable, and doesn’t change over time. 
  7.  The experimental probability it’s based on data and facts. In contrast, the theoretical probability it’s based on assumption. 
  8. The formula of experimental probability is the ratio of possible outcomes of a specific event to the total number of trials. In comparison, the formula of theoretical probability is the ratio of the number of suitable outcomes to the number of plausible outcomes.
References
  1. https://link.springer.com/content/pdf/10.1007/s11858-012-0469-z.pdf
  2. https://www.iejme.com/article/building-a-connection-between-experimental-and-theoretical-aspects-of-probability

Last Updated : 11 June, 2023

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