When we talk about probability, there are two main types of probability: experimental and theoretical. Experimental probability is the result of an actual experiment, while theoretical probability is what we calculate using mathematical models. In this post, we’ll explore the differences between these two types of probability and see how they’re used in different situations.

## What is Experimental Probability?

- Experimental probability is the likelihood of something occurring, as determined through experimentation or observation. It is often contrasted with theoretical probability, which is based on abstract models or hypothetical situations.
- For example, if a coin is flipped 100 times and lands on heads 50 times, the experimental probability of the coin landing on heads is 50%. However, the theoretical probability of a coin landing on heads is 50%, because there are an equal number of possible outcomes (heads or tails) and each outcome is equally likely to occur.
- In some cases, experimental probability and theoretical probability will coincide. In other cases, the experimental probability will deviate from theoretical probability due to factors such as chance or human error. Experimental probability can be a useful tool for making predictions about future events, but it is important to keep in mind that it is only an estimate.

## What is Theoretical Probability?

- Theoretical probability is the branch of mathematics that deals with the analysis of random phenomena. Theoretical probability seeks to answer questions such as “What is the likelihood of an event occurring?” or “What is the chance that a given event will occur?” Often, the theoretical probability is used to calculate the chances of something happening based on a model or theoretical situation. This type of probability is different from experimental probability, which uses actual data to calculate probabilities.
- Theoretical probability is often expressed as a percentage or ratio. For example, the theoretical probability of flipping a coin and getting a head is 50%. This means that if the coin were flipped an infinite number of times, one would expect to see a head half of the time. Similarly, the theoretical probability of rolling a die and getting a 6 is 1/6, or 16.7%.
- Theoretical probability can be used to make predictions about future events, but it cannot be used to predict specific individual events. This is because the theoretical probability is based on models and assumptions that may not reflect reality. As such, it should be used with caution and in combination with other information when making decisions.

## Difference between Experimental and Theoretical Probability

- Probability can be classified in two ways, experimental and theoretical. Experimental probability is based on an experiment or the observation of an event. Theoretical probability is calculated using mathematical formulas that predict the likelihood of an event occurring.
- Theoretical probability is calculated by taking the number of desired outcomes and dividing it by the number of possible outcomes. For example, if a coin is flipped 10 times, there is a 50% chance, or 1/2 probability, that it will land on heads 5 times.
- Experimental probability is based on observations. If a coin is flipped 100 times and lands on heads 52 times, then the experimental probability of the coin landing on heads would be 52%.
- It is important to note that as the sample size increases, the experimental probability should approach the theoretical probability. In other words, if a coin is flipped 1000 times, it should land on heads approximately 500 times if the probability of it landing on heads is 50%. If you flip a coin 100000 times, you should expect it to land on heads 50000 times if the theoretical probability is 50%. However, with smaller sample sizes, there may be a large discrepancy between experimental and theoretical probabilities.

## Conclusion

In conclusion, the difference between experimental and theoretical probability is that experimental probability is based on an actual experiment while theoretical probability is based on a calculated assumption. Both are important in understanding how likely something is to happen, but they provide different types of information.