In this chapter we will introduce the concept of probability and will also teach you important terms related to this chapter.

Note that it is very important concept as its method is widely used in daily life application.

## What is Probability ?

The word probability is made from term **” probable “** which mean **” likely to happen “**.

So, Probability basically tells you the **chance of happening any event through number**.

Using probability, the specialist tells;

(a) the chance of having rainfall today

(b) the chance of England wining the Football world cup

(c) the chance of getting head in coin toss

**Even the gambler use probability to bet their personal money in poker tournaments**.

Note that probability just tells you the likelihood of getting particular result. The actual results may or may not be the same.

I hope you understood the basic concept, let us look at some important terms related to the concept of probability.

### What is an experiment ?

The **task with well defined outcomes** is called experiment.

(a) Consider the task of tossing an unbiased coin. In this case there are two outcome possible, heads or tails.

(b) In task of throwing a dice, there are 6 possible outcomes from number 1 to number 6.

(c) In the task of determining the sex of child, there are two outcomes possible; a boy or girl.

### Random experiment

The **experiment whose outcome cannot be determined in advance** is called Random experiment.

For example, while tossing a coin, you cannot tell for sure if the head or tail will come.

Similar is the case with dice, you cannot be sure which number will come as final result.

### Deterministic experiment

The **experiment whose result can be determined in advance** is called deterministic experiment.

For example, In an experiment of choosing a triangle from multiple triangle figure, one can say for sure that for all triangle the ” sum of all angles is 180 degree “.

So no matter which triangle you choose, you can determined in advance that ” its sum of angle will be 180 degree”

### What is Sample space ?

The **collection of all possible outcome in a set** is called sample space.

**For example;**

(a) Consider the experiment of tossing an unbiased coin. We know that possible outcome will be head or tail.

The sample space is given as;

S = { H, T }

(b) Now consider experiment of throwing a dice. We know that possible outcome will be from 1 to 6.

The sample space is given as;

S = { 1, 2, 3, 4, 5, 6 }

**Note:**

The sample space is represented by ” S “

### What is event in probability ?

The **set of desirable outcome from given sample space** is called event.

Consider the experiment of throwing a dice, whose sample space (as discussed) is given below;

S = { 1, 2, 3, 4, 5, 6 }

Now if we desire outcome to get even number, this can be shown by event A.

Event A = { 2, 4, 6 }

So even A is the subset of Sample Space, which contain desired outcomes from given experiment.

Similarly, let there is event B which outcome for ” all odd number “

Event B = {1, 3, 5}

### Mutually exclusive events

Two events are said to be mutually exclusive, **if occurrence of one event prevent the occurrence of other event**.

For example;

Consider the experiment of throwing a dice.

Given below are two mutually exclusive events;

A = { ” getting even number ” }

B = { ” getting odd number ” }

Note that between event A & B there is no common element.

So if event A occurs, there is no chance that event B will also occur simultaneously.

### Exhaustive events

Two or more events are said to be exhaustive,** if their union will produce set of all possible outcomes (i.e. sample space )**

Consider the experiment of tossing an unbiased coin.

We know that there are two possible outcomes; head or tail. So the sample space is given as;

S = { H , T }

Let A be the event of getting a tails;

A = { T }

Let B be the event of getting heads;

B = { H }

If we take the union of event A & B, we will get the sample space;

A U B = { H, T }

Hence, the event A & B can be said as exhaustive events.

### Formula for determining probability

We have already said that the probability tells you the chance of happening any event.

The** formula for probability is given as**;

\mathtt{Probability\ =\frac{Number\ of\ favorable\ Outcomes}{Total\ possible\ outcomes}}

**Note:**

The value of probability always lie between 0 & 1.

If you want to get probability in percentage, multiply the value by 100.

Given below are some examples for conceptual understanding.**Example 01**

A coin is tossed once. What is the probability of getting heads?

**Solution**

While tossing a coin, one can get heads or tails.

The possibility of total outcomes is given in below sample space.

S = { H , T }

So number of total possible outcome = 2.

Let “A” be the event for getting heads.

A = { H }

So number of favorable outcome = 1

Using probability formula;

Probability = 1/2 = 0.5

The percentage value of probability is given as;

⟹ 0.5 x 100

⟹ 50%

So, the probability of getting heads is 50%.

Hence, there is 50% chance that one can get Heads while tossing an unbiased coin.