# Formula Sheets for General Aptitude (Part A): Probability

By Renuka Miglani|Updated : January 4th, 2023

General Aptitude Formula Sheets: During the preparation, the candidates study different formulas to solve problems, but at the last moment, these formulas might not be remembered by the candidates due to exam fear or pressure. We at BYJU'S Exam Prep do not want our students to lag anywhere during the preparation, so we have come up with a concept of a Formula Sheet that will help them revise the important formulas at the last moment. This formula sheet will be a short revision tool and contain only important formulas that need to be studied at the last minute to boost the score. Our experienced subject-matter experts have meticulously designed this CSIR NET General Aptitude Formula Sheet to provide you with the best authentic material.

In this article, we will cover the CSIR NET General Aptitude Most Important Formulas of Probability. Aspiring candidates can check all the most important formulas of the Mensuration for the last-minute revision. Scroll down the full article to find out!

## Formula Sheet On Probability

Random Experiments:

An experiment is called random experiment, if it satisfies the following two conditions:

(i) It has more than one possible outcome.

(ii) It is not possible to predict the outcome in advance.

Ex: When a dice is rolled, then on upper face one of the numbers 1, 2, 3, 4, 5 and 6 can appear, but we are not sure which one of these results will actually be obtained. This is a random experiment.

Outcomes: A possible result of a random experiment is called outcome.

Ex: When a die is rolled, then outcomes of this experiment are 1, 2, 3, 4, 5 or 6.

Sample Space: The set of all possible outcomes is called Sample Space.

Ex: When a die is rolled, then {1, 2, 3, 4, 5, 6} is the sample space of the experiment.

Equally likely events: When two or more events have equal chance of happening or equal probability of occurrence, then those events are called equally likely events.

Ex: When a fair die is rolled, then occurrence of 1 and occurrence of 2 are equally likely events.

Independent events: When two events are occurred, then the probability of occurrence of one event is not affected by the occurrence and non-occurrence of the other event, then the two invents will be called the independent event.

Ex: When a fair die is rolled and a card is picked from a well shuffled pack of cards, then occurrence of 3 when the fair die is rolled and picking a red card from the well shuffled pack of card are independent events because occurrence and non-occurrence of the one event is not affected by the occurrence and non-occurrence of the other event, then the these two invents are called the independent event.

Complementary events: When two events are occurred, such that if one of the events happens, then the other event cannot happen and vice versa.

Ex: When a fair die is rolled, then occurrence of odd number and occurrence of even numbers are complementary events.

Note: The probability of complement of an event must be unity minus the probability of the event.

Complementary event of event A is denoted by A' or A̅.

Exhaustive events: When two or more events are occurred. then all such that if one of the events happens, then the other event cannot happen and vice versa.

Ex: When a fair die is rolled, then occurrence of odd number and occurrence of even numbers are complementary events.

Mutually exclusive events: When two or more events are said to be mutually exclusive events, if occurrence of one of them precludes the occurrence of any of the remaining events. If events E1, E2 and E3 are mutually exclusive events, then

E1 Ç E2 Ç E3 = f

Ex: When a fair die is rolled, then event

E1 = Occurrence of the numbers less than 3

E2 = Occurrence of odd prime numbers

Sol: When a fair die is rolled, then

Sample space (S) = {1, 2, 3, 4, 5, 6}

E1 = {1, 2}

E2 = {3, 5}

Here E1 Ç E2 = f

Hence, E1 and E2 are mutually exclusive events.

Probability: Probability is possibility or chance of occurrence of the event.

P(E) =

Where: E is event

n(E) = Number of favorable cases to an event E.

n(S) = Sample space

Note: Probability of occurrence of event E is the ratio of a number of favourable cases to a total number of cases.

Ex: What is the probability of getting a jack from a well-shuffled pack of cards?

Sol: Here, n(S) = 52 and n(E) = 4 (Total 4 jacks)

Hence, required probability = P(E) = 4/52 = 1/13

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