Difference Between Experimental and Theoretical Probability

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 performing an experiment. In other words, it is the prospect of an event happening. 

Experimental vs Theoretical Probability

The main difference between experimental and theoretical probability is that experimental probability is based on the actual results of an experiment. In contrast, the theoretical probability is based on possible outcomes based on assumptions. Also, there is a difference in the formula too. In addition to that, in experimental probability, an experiment is performed to gather information, although, in theoretical probability, it does not happen.

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 collected 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 Between Experimental and Theoretical Probability 

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 experimenting repeatedly. Moreover, it focuses on what happened during an experiment rather than what would happen. 

Some specific outcomes are gathered before finding out the probability of a certain event. Besides, an experiment is conducted repeatedly to collect desired outcomes. Its basic approach is different from theoretical probability, although both find out probability. 

Probability-based on data and experiment results are often 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, 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 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 favorable 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 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, and several coins, etc.  

Lastly, the fothe 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 happening an event 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 to happen 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 chances 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, 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.  In 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. While the formula of theoretical probability is the formula is the ratio of the number of suitable outcomes to the number of plausible outcomes.

Conclusion 

Probability is the chance of occurring even with or without experimenting. Although, the final result may change drastically as several factors affect every situation. Yet, the prediction is made for what would happen. 

Experimental probability accounts for outcomes by experimenting repeatedly, then the chances of a specific event are found. Moreover, it accounts for facts and data of an experiment, although it also predicts what will happen in the future. It is reliable for certain situations such as batting averages, and other similar data of sports, predicting weather, etc. And, the formula of experimental probability is the ratio of possible outcomes of a specific event to the total number of trials.

Theoretical probability is the possibility of a certain event based on likely outcomes without experimenting. It is based on assumptions rather than facts and figures. Besides, it also predicts what will happen in the future. In addition to that, it is also considered reliable in certain situations such as coins flipping, spinners, etc. And the formula 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