There are various types of probabilities;

### 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.