Addition Rule of Probability

The third property of the probability states that probability of occurrence of either one or the other of two mutually exclusive events is equal to the sum of their individual probabilities.

For Example

Multiplication Rule

A probability may be calculated from the other probabilities.For example, joint parobability may be calculated as the product of appropriate marginal probability, and also from the conditional probability.This relationship of probabilities is called the multiplication rule of probability.

Joint Probability

When we decide to find the probability that a subject picked at random from group of subjects having features at the same time.Such probability is called joint probability.
Lets us the following table

Conditional Probability

The set of all outcomes constitute a subset of complete group. We can say the size of the group of intrest may be reduced by conditions not applicable to the group. When the prrobabilities are computed or calculated with a subset of the total group as the denominator, the result is a conditional Probability.
Example:-

Calculation of Probabilityof an Event

Now we use the probability techniques to calculate the probabilities of some events.
Example:-

Properties of Probability

Russian mathematician  A. N. Kolmogrov, in 1933 formalized the axiomatic approach to probability.
This approach has the following three main properties;

Subjective Probability

In early 1950 L.J. Savage gave considerable impetus to "Personalistic". it is the Subjective concept of the Probability.

Relative Frequency Probability

It is the approach to chance or probability of some process and ability to calculate the number of repetitions and also the number of times of some  event of interest occurs.

But keep in your mind that m/n is only the estimate of the P(E).

Classical Probability

The term clasical probability was firstly used by the two mathematicians;
i) Pascal
ii) Fermat
This theory was used to develop attempts to solve the problems which are related to the game of chance. For example the rolling of dice.

Definition of classical Probability