Theoretical probability is the theory behind probability, as the name implies. Based on mathematics and reasoning, theoretical probability predicts the outcome of an event. Without doing any trials, it informs us what should happen in an ideal circumstance. Theoretical probability is highly beneficial in instances when doing an actual experiment to get a sound conclusion is not possible, for as when launching a satellite.

## Definition

Theoretical probability is a method of calculating the likelihood of a certain event’s outcome in probability theory. Probability theory is an area of mathematics concerned with determining the chance of a random event occurring. The likelihood of an event occurring ranges from 0 to 1. If the probability is near zero, it means the occurrence is less likely to occur. Similarly, if the probability is closer to 1, the event has a better chance of happening.

The number of favourable outcomes divided by the entire number of alternative outcomes is theoretical probability. There is no need to do an experiment to ascertain the theoretical probability. However, understanding about the context is necessary to determine the likelihood of that event occurring. Theoretical probability estimates the likelihood of an event occurring based on the assumption that all occurrences are equally likely to occur.

## Example of Theoretical Probability

Assume there are five cards in total, and you need to calculate the chance of drawing two of them. The number of favourable possibilities (2) is then divided by the total potential outcomes (5) to provide a chance of 0.4 using the idea of theoretical probability.

Theoretical Probability Formula:

Using logical reasoning or a simple formula, the theoretical probability may be computed. The quantity of alternative possibilities determines the outcome of this sort of probability. The ratio of the number of favourable outcomes to the total number of likely outcomes is the theoretical probability formula. This formula is stated as follows:

Theoretical Probability = The number of favourable outcomes / the total number of possible outcomes

How to calculate theoretical probability?

Without doing any tests, the theoretical probability is used to represent the possibility of an event occurring. Let’s say an individual owns 30 raffle tickets and 500 tickets were sold in total. The following are the steps to calculating the theoretical likelihood of someone receiving a prize:

Step 1: Determine how many positive outcomes there are. Because there are 30 raffle tickets, the number of desirable outcomes will be 30.

Step 2: Compile a list of all probable outcomes. Since 500 total tickets were sold, the total number of potential outcomes will be 500.

Step 3: Divide the result from step 1 by step 2 to get the theoretical probability. As a result, 30/500 = 0.06. This indicates that the chance of winning a raffle prize is 0.06.

Empirical Probability vs. Theoretical Probability:

Experimental probability is another name for empirical probability. Both theoretical and empirical probability are methods for calculating the likelihood of a random event occurring.

Theoretical Probability | Empirical Probability |

The theory underpinning probability is known as theoretical probability. | The probability estimated using historical data is known as empirical probability or experimental probability. |

There are no experiments to determine the theoretical probability. Rather, it portrays what is supposed to occur. | The outcome of an experiment is empirical probability. |

It may be predicted by logical thinking and understanding of the circumstance. | Experiments are repeated and various results are observed to ascertain it. |

The following is the theoretical probability formula: Theoretical Probability is defined as the number of favourable outcomes divided by the total number of alternative outcomes. | The following is the empirical probability formula: Empirical Probability = Total number of trials divided by the number of times an event happens. |

A fair coin is tossed as an example. P(Head) = 1 / 2 = 0.5 is the probability of receiving a head. P(Tail) = 1 / 2 = 0.5 is the probability of receiving a tail. | For instance, after tossing a fair coin 15 times, a head shows 5 times and a tail appears 3 times. P(Tail) = 3 / 15 = 0.2 P(Head) = 5 / 15 = 0.33 |

Points to Remember:

- Without doing an experiment, the theoretical probability is used to calculate the chance of an event occurring
- Theoretical probability holds that all occurrences have the same chance of happening
- The theoretical probability formula is The number of favourable outcomes / the total number of possible outcomes

### Conclusion:

Theoretical probability is a type of probability that is calculated using logic. Experimental probability is a type of probability that is calculated using the outcomes of a series of experiments.