# Probability Problems and Probability Formulas for IBPS PO and SSC CGL Exam

In this post we will discuss Probability Formulas and will solve Probability Problems for IBPS PO and SSC CGL Exams

In SSC CGL and IBPS PO, Problems based on Probability Formulas are always asked. These are the simplest set of problems that can be solved by using Probability Formulas. The word probability is the synonym of the word 'chance' which is frequently used in day to day life. The word probability is used in a broad sense to indicate the possibility of something to happen. By the means of Probability formulas, we measure all the possible different types of events that can occur.

In this post, we will discuss different terminologies that are used while solving probability problems and will solve Probability problems using probability formulas.

Terms Required to solve Probability Problems

Experiment is an operation or an event which can get well-defined outcomes.

An experiment whose outcome or result cannot be predicted even though all possible outcomes are known in advance is called as a Random experiment.
For example: tossing a coin, throwing a dice etc.
When we toss a coin, we know there are two possible outcomes but still, we cannot predict the possibility.
A dice has got six faces, and each face has one integer on it, even after knowing all the possibilities we cannot predict the possible outcome.
The set of all possible outcome of a random experiment is called as Sample Space. It is denoted by ' S.'
In the case of a coin, Sample Space is the two possible outcomes i.e., Head and Tails.
In the case of a dice, Sample Space is the six possible outcomes i.e., 1, 2, 3, 4, 5, and 6.

Every single element in the Sample Space is called as Sample Point.

List of Probability Formulas to solve Probability Problems

Probability of an event "E" is denoted  as P(E)  where,
P(E) - Number of favourable outcomes / Total Number of Outcomes
P(E̅ ) - Number of Unfavourable outcomes / Total number of outcomes
Probability of the success of an event 'E' is P(E)
Probability of the failure of the event 'E' is P(E)
Odds in the favour of an event 'E' =P(E) /P(E)
Odds against the event 'E'= P(E)/P(E)
Module 1: How to solve Probability Problems when a Coin is Tossed
Example 1: Probability Problems solved using Probability Formula when two coins are tossed simultaneously

Question: When two coins are tossed simultaneously, what is the possibility that both the coins show heads?

Solution:
Step 1:
First, find the sample space of the given question.
S = { (H.T) , (T, H) (H,H) , (T, T) }

Step 2:
The possibility that the two coins show heads are,
P(H.H) = n(E)/n(S)

Step 3:
P(H,H) = 1/4

Therefore, 1/4 is the possibility that the two coins will show Heads.

Example 2: Probability Question solved using Probability Formulas when three coins are tossed simultaneously

Question: When three coins are tossed, What is the possibility that two coins show tails as output?

Solution:
Step 1:
First, let's write down all the possible outcomes i.e. Sample Space
S = { (H, H, H), ( T, T, T), (H, H, T), ( H, T, H), (T, H, H), (H, T, T), (T, H, T) ,(T ,T, H) }

Step 2:
To find the probability of that two coins show tail as the output when three coins are tossed
P(E) = n(E)/n(S)

Step 3:
By substituting the values in the formulas,
P(E) = 3/8

Therefore, the probability of two coins to tail as output when three coins are tossed simultaneously is 3/8

Module 2: How to solve Probability Problems When a dice is rolled

Example 1: Probability Problems solved using Probability Formula when an unbiased dice is rolled.

Question: When an unbiased dice is rolled, what is the possibility that the output is
(i)  1       (ii) 2      (iii) a prime number      (iv)  >2

Solution:
Step 1:
First, write down all the possible probability to solve all the probability problem.
S ( 1, 2, 3, 4, 5, 6)

Step 2:
Now, write the probability formula to find out all the answers to the question.
P(E) = n(E)/n (S)

Step 3:
Substitute the values in the above formula.

(i)  Probability of 1 being the output is
P(1) = 1/6

(ii) Probability of 1 being the output is
P(2) = 1/6

(iii) Probability of the output being a prime number is
P(a prime number) = 3/6 = 1/2

(iv) Probability of a number being greater than 2 is
P (>2) = 4/6 = 2/3

Example 2: How to solve Probability Problems When two dice are rolled simultaneously

Question: When two dice are rolled together, what is the possibility that the sum of the output is 8?

Solution:
Step 1:
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)}

Step 2:
Probability formula,
P(E) = n(E)/n(S)

Step 3:
Substitute the values in the probability formula
P(8) = 5/36

Therefore, the probability of 8 to be the outcome when two dice are rolled is 5/36.

Do write in the comment section how this post helped you to learn the Probability Formulas and solve probability Problems.

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