Introduction

The branch of mathematics that measures the uncertainty of the occurrence of an event using numbers is called probability. 

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.

Trial

A trial is an action which results in one or several outcomes, for example each toss of the coin and each throw of the die are called trials

Independent Trial

:Successive trials of some random event for example tosses of a coin,throws of a die are said to be independent if the outcome of any one trial does not impact the outcomes of any others.

Sample space

It is a set of all possible outcomes of an experiment.

e.g. when we coin is tossed, the possible outcome are Head and Tail. So sample space is Head and tail

There are two types of approaches to study probability.

1. Experimental or Empirical Probability

The result of probability based on the actual experiment is called experimental probability. In this case, the results could be different if we do the same experiment again.

\mathrm{P(E)=\dfrac{Number\ of\ the\ trials\ in\ which\ the\ event\ happened}{Total\ number\ of\ trials}}

2. Probability — A Theoretical Approach

In the theoretical approach, we predict the results without performing the experiment actually. The other name of theoretical probability is classical probability.

\mathrm{P(E)=\dfrac{Number\ of\ outcomes\ favourable\ to\ F}{Number\ of\ all\ possible\ outcomes}}

Where the outcomes are equally likely.

Equally Likely Outcomes

If we have the same possibility of getting each outcome then it is called equally likely outcomes.

Example

A dice have the same possibility of getting 1, 2, 3, 4, 5 and 6.

Not Equally Likely

If we don’t have the same possibility of getting each outcome then it is said to be the not equally likely outcome.

Example

3 green balls and 2 pink balls are not equally likely as the possibility of the green ball is 3 and the possibility of the pink ball is 2.

Elementary Event

If an event has only one possible outcome then it is called an elementary event.

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