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# PROBABILITY

## PROBABILITY

###### By / Feb 13, 2019

An important topic with questions based on pure logic, it is increasingly gaining importance in Management Entrance examinations.

Let us start by observing some natural phenomena:
- Sun rises in the East.
- It’s cloudy, hence, it might rain today

Can we find a base to classify these phenomena?
We may, as we know the first is a definite phenomenon and the second is not; as we are not sure whether it shall rain today or not, i.e. we are in a situation of uncertainty.
A definite situation or phenomenon is known as “DETERMINISTIC” phenomenon.
An uncertain situation or phenomenon is known as “PROBABILISTIC” phenomenon.

In the same manner, Experiments (operations done resulting in some final outcomes) are of two types:
a) Experiment with a definite outcome.
b) Experiment in which required outcome may be any one of the possible outcomes.

Choosing a red card out of a suit of “Hearts” is a definite outcome.
Choosing a red card out of a pack of cards may have the required outcome as any of the possible outcomes.
Experiments of the second kind are called “RANDOM EXPERIMENTS(RE)
One instance of a Random Experiment is called a Trial.
The set of all possible outcomes for a particular Random Experiment is called its Sample Space (S).
Sample Space (S) is analogous to “Universal Space” in Set Theory.
E.g. for an experiment of tossing a coin, the sample space is the set of two outcomes- Heads and Tails.
Any subset of a sample space is called a Simple Event.
2 or more events which occur for two or more different experiments or for 2 or more trials of the same experiment are called Compound Events.
E.g If a coin is tossed and a die is rolled, the event of getting a tail in a toss of a coin and 6 in a roll of a die is a Compound Event.
Similarly, if a coin is tossed twice, the event of getting Heads on the first toss and a Tails on the second toss is a Compound Event.

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Last updated on : Mar 24, 2023

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