# Probability – Aptitude Questions and Answers

Are you preparing for a job interview, or an entrance exam, or just want to improve your quantitative skills? If so, then it is important to have a good understanding of probability and how it works. Probability is a integral part of mathematics and plays a crucial role in fields like science, engineering, finance, and economics. In this article, we will discuss the most common types of probability questions which are commonly asked on quantitative aptitude tests. Whether you are preparing for a job interview, an entrance exam, or simply looking to sharpen your quantitative skills, this article will help you gain a deeper understanding of probability and its applications in Quantitative Aptitude.

## Probability Formulas

Here are some basic probability formulas that are frequently used in quantitative aptitude exams, along with a table for quick reference:

### Description

P(A or B) = P(A) + P(B) – P(A and B)

Probability of the union of two events

P(A and B) = P(A) x P(B|A) = P(B) x P(A|B)

Probability of the intersection of two events

P(A|B) = P(A and B) / P(B)

Conditional probability

P(B|A) = P(A and B) / P(A)

Conditional probability

P(A’) = 1 – P(A)

Probability of the complementary event

P(A) + P(A’) = 1

Probability of the sample space

P(A and B) = 0 if A and B are mutually exclusive events

Probability of two mutually exclusive events

P(A and B) = P(A) x P(B) if A and B are independent events

Probability of two independent events

P(A and B) > P(A) if A and B are dependent events

Probability of two dependent events

P(A) x P(B) ≤ P(A and B) ≤ min(P(A), P(B))

Inequality for the probability of intersection

P(A or B or C) = P(A) + P(B) + P(C) – P(A and B) – P(A and C) – P(B and C) + P(A and B and C)

Probability of the union of three events

Note: P(A) represents the probability of event A. P(B|A) represents the probability of event B given that event A has occurred. P(A and B) represents the probability of both events A and B occurring.

#### Practice Quiz:

Practice Probability Aptitude Quiz Questions

## Sample Questions on Probability

### Question 1 : Three unbiased coins are tossed. What is the probability that atmost one head occurs ?

Solution

S = {HHH, HHT, HTH, THH, HTT, THT, TTH, TTT} Favorable outcomes = {HTT, THT, TTH, TTT} Total number of outcomes = 8 Number of favorable outcomes = 4 Required probability = 4 / 8 = 0.50

### Question 2 : Find the probability of getting a red card when a card is drawn from a well shuffled pack of cards.

Solution

Total number of outcomes = 52 Number of favorable outcomes = Number of red cards = 26 => Required probability = 26 / 52 = 0.50

### Question 3 : A bag contains 6 white and 4 black balls. Two balls are drawn at random from the bag. Find the probability that both the balls are of the same color.

Solution

Outcome will be favorable if the two balls drawn are of the same color. => Number of favorable outcomes = 6 C 2 + 4 C 2 = 21 Total number of outcomes = 10 C 2 = 45 Therefore, required probability = 21 / 45 = 7 / 15

### Question 4 : An unbiased die is tossed. Find the probability of getting an even number.

Solution

S = {1, 2, 3, 4, 5, 6} Favorable outcomes = {2, 4, 6} Required probability = 3 / 6 = 0.50

### Question 5 : From a bag containing red and blue balls, 10 each, 2 balls are drawn at random. Find the probability that one of them is red and the other is blue.

Solution

Total number of outcomes = 20 C 2 = 190 Number of favorable outcomes = 10 C 1 x 10 C 1 = 100 Therefore, required probability = 100 / 190 = 10 / 19

## Related Resources:

Problems on Probability | Set-2

Test your knowledge of Probability in Quantitative Aptitude with the quiz linked below, containing numerous practice questions to help you master the topic:-

## Also Practice:

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