## Introduction : Probability

#### Event –

An **Event **is a set of outcomes. For example when we roll dice the probability of getting a number less than five is an event.Note: An Event can have a single outcome.

#### Outcome –

An Outcome is a result of a random experiment. For example, when we roll a dice getting six is an outcome.

#### Experimental probability-

Experimental probability can be applied to any event associated with an experiment that is repeated a large number of times.

#### Empirical probability –

** **A trial is when the experiment is performed once. It is also known as empirical probability**.**

### Experimental or empirical probability: P(E) =Number of trials where the event occurred/Total Number of Trials

#### Theoretical probability-

Here we assume that the outcomes of the experiment are** **equally likely**.**

P(E) = Number of Outcomes Favourable to E / Number of all possible outcomes of the experiment

#### Elementary event –

An event having only one outcome** **of the experiment is called an elementary** **event. Example: Take the experiment of tossing a coin n number of times. One trial of this experiment has two possible outcomes: Heads(H) or Tails(T). So for an individual toss, it has only one outcome, i.e Heads or Tails.

#### Sum of probabilities-

The** **sum of the probabilities of all the elementary events of an experiment is one.

Example: take the coin-tossing experiment. P(Heads) + P(Tails )

(1/2)+ (1/2) =1

#### Impossible event-

An event that has** **no chance of occurring** **is called an Impossible event, i.e. P(E) = 0.E.g: Probability of getting a 7 on a roll of a die is 0. As 7 can never be an outcome of this trial.

#### Sure event-

An event that has a 100% probability of occurrence is called a **sure event**. The probability of occurrence of a sure event is **one**.E.g: What is the probability that a number obtained after throwing a die is less than 7?

So, P(E) = P(Getting a number less than 7) = 6/6= 1

#### Range of Probability of an event-

The range of probability of an event lies between 0 and 1 inclusive of 0 and 1, i.e. 0≤P(E)≤1.

#### Geometric probability-

Geometric probability is the calculation of the likelihood that one will hit a particular area of a figure. It is calculated by dividing the desired area by the total area. In the case of Geometrical probability, there are infinite outcomes.

#### Complimentary events-

Complementary events are two outcomes of an event that are the only two possible outcomes. This is like flipping a coin and getting heads or tails. P(E)+P(¯E)=1, where E and ¯E are complementary events. The event , representing ‘**not E**‘, is called the **complement** of the event **E**.