**Introduction to Probability**

**Introduction to Probability**

**Probability**

- Probability is the measure of the likelihood of an event to occur. Events canâ€™t be predicted with certainty but can be expressed as to how likely it can occur using the idea of probability.
- Probability can range between 0 and 1, where 0 probability means the event to be an impossible one and probability of 1 indicates a certain event.

**Experiment**

An experiment:

- is any procedure that can be infinitely repeated or any series of actions that have a well-defined set of possible outcomes.
- can either have only one or more than one possible outcomes.
- is also called the sample space.

**Trail**

- A single event that is performed to determine the outcome is called a trial.
- All possible trials that constitute a well-defined set of possible outcomes are collectively called an experiment/sample space.

Experimental Probability

**Experimental/Empirical Probability**

The empirical probability of an event that may happen is given by:

Probability of event to happen P(E)=Number of favourable outcomes/Total number of outcomes

**Coin Tossing Experiment**

Consider a fair coin. There are only two possible outcomes that are either getting heads or tails.

Number of possible outcomes = 2

Number of outcomes to get head = 1

The probability of getting head =Number of outcomes to get head/Number of possible outcomes=1/2

**Rolling of Dice Experiment**

When a fair dice is rolled, the number that comes up top is a number between one to six. Assuming we roll the dice once, to check the possibility of three coming up.

Number of possible outcomes = 6

Number of outcomes to get three = 1

The probability of getting three = Number of outcomes to get three/Number of possible outcomes=1/6

**Sum of Probabilities of Favorable and Unfavourable events**

- When a trial is done for an expected outcome, there are chances when the expected outcome is achieved. Such a trial/event is called a favourable event.
- When a trial is done for an expected outcome, there are chances when the expected outcome is not achieved. Such a trial/event is called an unfavourable event.
- All favourable and unfavourable event outcomes come from the well-defined set of outcomes.
- Suppose an event of sample space S has n favourable outcomes. Then, there are S-n, unfavourable outcomes.
- The probability of favourable and unfavourable events happening depends upon the number of trials performed. However, the sum of both these probabilities is always equal to one.