**Quantitative Aptitude Probability Study Material**

Human life is full of uncertainties. In our day to day life we very often make guess and give statements like : Possibility of a particular party to win this election is more”. Most probably it will be sunny day today ’’; “It is almost certain that Ramesh will compete in Bank P.O. Exam.” Whenever we use such statements we have intuition which enables us to claim that one event is more likely to happen than the other. In probability theory, the degree of certainty and uncertainty is measured in terms of numbers lying between 0 and 1.

SOME BASIC CONCEPTS

1. Experiment: An operation which results in some well defined outcomes is called an experiment.

2. Random Experiment: An experiment whose outcome cannot be predicted with certainty is called a random experiment. In other words if an experiment is performed many times under similar conditions and the outcome each lime is not the same, then this experiment is known as a random experiment.

Remark : An experiment whose outcome cannot be predicted before hand is not a random experiment. For example, when we throw an apple upward, it is certain that it will come to the earth falling downward. So, throwing an apple upward is not a random experiment

Examples : (i) ‘Tossing of a fair coin” is a random experiment because if we toss a coin either a head or a tail will come up. But if we toss a coin again and again, the outcome in each case will not be the same. –

(ii) “Drawing a card from a well shuffled pack of 52 playing cards” is a random experiment.

(iii) ‘Throwing an unbiased dice” is a random experiment since when we throw a dice, we cannot say with certainty that a particular number ranging from 1 to 6 will come up.

3. Trial and Elementary Events: When an experiment is repeated under similar conditions and it does not give the same result each time but may result in any one of the several possible outcomes, the experiment is called a trial and the outcomes are called cases. The number of times the experiment is repeated is called the number of trials.

For examples,

(i) Tossing of a coin is a trial and getting a head or a tail is case or elementary event. .

(ii) Throwing of a dice is trial and getting 3 on its upper face is an elementary event or case.

(iii) One toss of a coin is a trial when the coin is tossed 5 times.

(iv) Drawing a card from a pack of a well shuffled cards is a trial and getting a king of diamond is an elementary event.