##### Introduction to Probability and Some basic definitions.

Let's start with the basics:

**What is the probability ?**

Informally, the probability is all about representing your chances of success or failure with the help of mathematics. It is a mathematical measure of degree randomness.

Some important terms:

**Random Experiment:-**

When we perform any task, we actually know all the outcomes but we don't know what outcome will come in advance. for example:

When we toss an unbiased coin, we know either head or tail will show up but we don't know what comes when? This is called a random experiment.

**Sample Space:** Set of all possible outcomes of an experiment. Example:

1.When you toss a coin

Sample Space will be {head, tail}

2. When you roll a dice

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

Note: Sample space is a set. It means you can't repeat things inside a sample space.

**Events: **Subset of sample space is called Events. Example:

1. When you toss a coin getting ahead is or getting a tail is a subset of Sample Space.

2. On rolling a dice "getting even no " is an event.

**Mutually Exclusive events:**

Two Events E1 and E2 are said to be mutually exclusive if

**E1 ∩ E2 = Ø**

**Independent Events: **Two events are said to be independent if happening of one event doesn't affect another event. Example:

When you toss 2 coins getting head on the first coin is not going to affect getting anything on the second coin. So Both are independent events.

**Some Rules:-**

For each event E in a sample Space S, we assign a number P(E) Such that

1. 0 <= P(E) <= 1

2. P(S)= 1 = P(E) + P(E^{c})

3. For any sequence of events E1, E2 ......E_{n} that are mutually events then

P(E1∪ E2 ∪ E3 ∪...... ∪ E_{n}) = P(E1) + P(E2) + P(E3) +......... P(E_{n})

**Probability of happening of an event E is**=

Total number of favorable outcome / Total number of possible outcomes

OR

**P(E) = favourable outcome / possible outcomes**

- Probability of an impossible event is always O
- Probability of a certain event is always 1.

Example:

1.On tossing a coin find the probability of getting a head.

Solution:

When you toss a coin Possible sample space is

S= {H, T}

P(getting a head ) = 1 / 2

P (getting a tail ) = 1 /2