# The four Types of Probability

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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 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

Or

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

Where;

• 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.

#### Example;

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

#### Solution.

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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