The four Types of Probability

Defining Probability types

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There are various types of probabilities;


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1. Classical Probability

The classical probability states that in a situation where there are A outcomes that are equally likely to happen and event B has specifically C of these outcomes, the probability of B is C/A, or P(B)=C/A. For example, there are only six possible outcomes when rolling dice. So, the probability of rolling each number is 1/6.

2. Empirical Probability

The empirical probability, also known as experimental probability, explains the likelihood of an outcome through experiments.

For example, suppose you are tossing a weighted die with no idea which side has much weight to have an idea of the possibility of each outcome. In that case, you can toss the die a couple of times while recording the proportion of time a certain outcome is achieved and then estimate the probability of that outcome.

Probability of event P(E) = The Number of times that event occurs / total number of trials.

3. Subjective Probability

Subjective probability is based on own personal judgment and belief that an event will occur. It is the probability that an event that a person expects will occur based on their knowledge without any formal calculations.

For example, investors who trade in stock can predict that the price of the stock will fall at a certain month or a football fan can predict a certain team will win based on their past wins or losses or by analyzing their opponents.

4. Axiomatic Probability

Axiomatic probability

Axiomatic probability uses axioms or a set of rules. You can quantify the non-occurrence or occurrence of the events in this probability. The possibility of an outcome or event is established through occurrences of previous outcomes or events.

The Probability Formula

The probability formula is used to calculate the probability of occurrence of an event.

Probability Formulas

The formula for an event probability is;

P(A) = Number of favorable outcomes / Total no. of favorable outcomes


P(A) = n(A) / n(S)


  • P(A) is the probability of an outcome or event
  • n(A) is the number of favorable outcomes
  • n(S) is the sum of events in the sample.

The outcome of interest is the favorable outcome.


What probability will an Ace card be picked from a standard deck?


The standard pack has 52 cards.

There are 4 Ace cards in a deck of cards

Henceforth, the favorable outcome will be 4

Applying the formula;

P(Ace) = (no. of favorable outcomes) / (Total no. of favorable outcomes)

P(Ace) = 4/52 = 1/13

Therefore, the probability of picking an Ace is 1/13.

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