Finite Probability is a very important concept in discrete mathematics. Before we begin let’s understand some basic terminology, that is important in understanding probability theory.

### Basic Terminologies

#### Experiment

THROW A DICE AND YOU GET A NUMBER |

Sample Space

#### Event

Probability of an event is denoted as P(E) and 0 < = P(E) <= 1.

#### Favorable Outcome

When an event occur then it is a favorable outcome when it happens.

#### Unfavorable Outcome

When the event does not happen then it is an unfavorable outcome as it did not happen. Sometimes, we also need to find unfavorable outcomes of an event.

#### Equally likely

An event is equally likely if the probability of each outcome in sample space is equally likely.

For example, when we toss a coin we get either Head or Tail out of two outcomes of the sample space. So there is a 50-50 chance of getting a Head or Tail and both are equally likely events.

HEAD OR TAIL ARE EQUALLY LIKELY EVENTS |

### Formal Definition of Probability

If S is a finite non-empty sample space of equally likely outcomes and E is an event, that is, a subset of S, then the probability of E is

P(E) = |E| / |S|

### Example Problem

**Question :**

**
** A box contains 3 Red balls and 5 Green balls. What is the probability that a ball picked randomly from the box is Red?

**Solution :**

Total Number of Balls in Box = 3 + 5 = 8

Sample Space = 8

There are 3 ways to pick Red balls, Therefore, Event E = 3

**P(E) = 3/8**

The probability of picking a Red ball from the box is 3/8.