**Event and outcome**

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

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.

To know more about Types of Events, visit here.

**Experimental Probability**

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

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

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**Theoretical Probability**

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

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

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**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.

**Complementary 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 E¯, representing ‘**not E**‘, is called the **complement** of the event **E**.