3.1.3. Types of Probability

There are three main types of probability: classical probability, empirical probability, and subjective probability.

Classical probability : Classical probability, also known as a priori probability, is based on the assumption of equally likely outcomes. This means that if there are n possible outcomes, each outcome has an equal chance of occurring, and the probability of an event is the ratio of the number of favorable outcomes to the total number of possible outcomes. For example, the probability of rolling a six on a fair die is 1/6, because there is only one favorable outcome out of six possible outcomes.

Empirical probability : Empirical probability, also known as experimental probability, is based on observation or experimentation. It involves conducting a series of trials and counting the number of times an event occurs. The probability of an event is then estimated as the ratio of the number of times the event occurs to the total number of trials. For example, if a coin is tossed 100 times and comes up heads 56 times, the empirical probability of getting heads is 56/100 = 0.56.

Subjective probability : Subjective probability, also known as personal probability, is based on personal judgments or beliefs. It is used when there is no empirical or classical basis for determining probabilities. In subjective probability, an individual assigns a probability based on their own degree of belief or confidence in an event occurring. For example, a person might assign a subjective probability of 0.8 to the likelihood of rain tomorrow based on their own judgment and experience.

Each type of probability has its own strengths and weaknesses, and they are used in different situations depending on the available information and the context of the problem. Classical probability is useful when all outcomes are equally likely, while empirical probability is useful when there is data available from past experiments or observations. Subjective probability is useful when there is no empirical or classical basis for determining probabilities and relies on personal judgments or beliefs.