Probability Formula

Introduction to Probability Formulas with Examples

You must have heard the term “probability” been coined for predicting the weather forecast in news TV bulletin for the next few days for some parts of the country. For calculating the probability of different types of situation, probability formula and its related basic concepts are used. Probability is the way to measure the uncertainty of how likely an event has happened or bound to happen.

There are few crucial terminologies which are associated with all probability formulas.

• Experiment: Any situation or a phenomenon like tossing a coin, rolling dice, etc.

• Outcome: The result of an event after performing an experiment like the side of the coin after flipping, the number appearing on dice after rolling and a card is drawn out from a pack of well-shuffled cards, etc.

• Event: The combination of all possible outcomes of an experiment like getting head or tail on a tossed coin, getting even or odd number on dice, etc.

• Sample Space: The set of all possible results or outcomes.

• Probability Function: The function helps in obtaining the probability of each and every outcome.

• Probability Formulas with Examples

The probability formula provides the ratio of the number of favorable outcomes to the total number of possible outcomes

The probability of an Event = (Number of favorable outcomes) / (Total number of possible outcomes)
P(A) = n(E) / n(S)
P(A) < 1

Here, P(A) means finding the probability of an event A, n(E) means the number of favorable outcomes of an event and n(S) means set of all possible outcomes of an event.

If the probability of occurring an event is P(A) then the probability of not occurring an event is

P(A’) = 1- P(A)

Vedantu provides a better understanding of the basic probability formulas with an example

Example 01: Probability of obtaining an odd number on rolling dice for once.

Solution: Sample Space = {1, 2, 3, 4, 5, 6}
n(S) = 6
Favorable outcomes = {1, 3, 5}
n(E) = 3
Using the probability formula,

P(A) = n(E) / n(S)

P(Getting an odd number) = 3 / 6 = ½ = 0.5

Important list of probability formulas

Event (A OR B)
P (A U B) = P (A) + P (B) – P (A ∩ B)

Event (A AND B)
P (A ∩ B) = P (A) . P (B)

Event (A NOT B)
P(A NOT B) = A – B

Event (B NOT A)
P(B NOT A) = B – A

Event (NOT A)

Probability of occurrence of an event is P(A)

Probability of non-occurrence of the same event is P(A’).

Some probability important formulas based on them are as follows:

• • P(A.A’) = 0

• • P(A.B) + P (A’.B’) = 1

• • P(A’B) = P(B) – P(A.B)

• • P(A.B’) = P(A) – P(A.B)

• • P(A+B) = P(AB’) + P(A’B) + P(A.B)

• Example 01: Two dice are rolled simultaneously. Calculate the probability of getting the sum of the numbers on the two dice is 6.

Solution: Sample Space = [{(1, 1), (1, 2), (1,3), (1,4), (1,5), (1, 6)} {(2, 1), (2, 2),(2,3), (2,4), (2,5), (2, 6)} {(3, 1), (3, 2), (3,3), (3,4), (3,5), (3, 6)} {(4, 1), (4, 2), (4,3), (4,4), (4,5), (4, 6)} {(5, 1), (5,2), (5,3), (5,4), (5,5), (5, 6)} {(6, 1), (6, 2), (6,3), (6,4), (6,5), (6, 6)}] n(S) = 36 Favorable outcomes = {(1, 5), (2, 4), (3, 3), (4, 2) and (5, 1)} n(E) = 5

Using, P(A) = n(E) / n(S)

P(Getting sum of numbers on two dice 6) = 5/ 36

What to expect from Vedantu?

Vedantu has a list of basic and advanced probability formulas essential in every syllabus for class 6 to 12

• • Students can access the free of cost formulae anytime.

• • Chapter-wise math formulae can be downloaded in PDF format by Students from class 6 to 12.

• • The important revision notes, sample papers, study materials and questions to practice can be accessed by students for learning.

• • A unique methodology is being adopted by Vedantu for solving different math problems. This way students can be able to understand the basics of problem and solution easily without any confusion.

• Students can access the essential study materials from Vedantu like RS Aggarwal Solutions, RD Sharma solutions, NCERT solutions, etc. These solutions can be helpful in enhancing the concepts of probability and the application of every formula.

For practice

Two dice are thrown simultaneously. The probability of getting even numbers on both the dice is
a. $\frac{1}{4}$ b. $\frac{3}{4}$ c. $\frac{2}{{35}}$ d. $\frac{{11}}{{36}}$