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Class 10 Math Chapter 14
Probability
Important Questions

Here are some essential questions for Class 10 Mathematics Chapter 15, Probability, thoughtfully chosen to aid students in their preparation for the CBSE Class 10 Mathematics Examination in 2024-25. By practicing these varied problems, students can enhance their comprehension of Probability concepts and refine their problem-solving skills.

Table of Contents

Introduction

In Chapter 14 of Class 10 Mathematics, Probability, we will delve into the Classical Definition of Probability. This concept allows us to quantify the likelihood of an event occurring by comparing the number of favorable outcomes to the total possible outcomes. Additionally, we will solve simple problems to determine the probability of specific events.

What is probability?

Probability is a measure that quantifies the likelihood of an event occurring. It is expressed as a value between 0 and 1, where 0 represents an impossible event, and 1 represents a certain event. Probability helps us understand and predict outcomes in various situations.

Class 10 Probability Important Questions and Answers

Q1. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will NOT be an ace is :

Options

$(a)\dfrac{1}{13}\\[6.5 bp] (b) \dfrac{1}{4}\\[6.5 bp] (c) \dfrac{12}{13}\\[6.5 bp] (d) \dfrac{3}{4}$

Ans.(c) $\dfrac{12}{13}$

Explanation:
Total number of possible outcomes = 52
Number of aces in the pack = 4
Thus, the probability of not drawing an ace
$\therefore P(E) = \dfrac{52-4}{52} = \dfrac{48}{52} = \dfrac{12}{13}$

Q2. A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. What is the probability of getting a black ball ?

Options

$(a) \dfrac{2}{5}\\[4.5 bp] \text{(b) }\dfrac{3}{5}\\[4.5 bp] \text{(c) }\dfrac{1}{10}\\[4.5 bp] \text{(d) None of these}$

Ans. (b) $\dfrac{3}{5}$

Explanation:
Total number of possible outcomes = 10
The total number of favourable outcomes = 6
$\therefore P(E) = \dfrac{6}{10} = \dfrac{3}{5}$

Q3. A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.

Explanation:
The number of cards =52
Number of kings and queens=4+4=8
Thus, number of favourable outcomes
= 52−8 = 44
$\therefore P(E) = \dfrac{44}{52} = \dfrac{11}{13}$

Q4. A card is drawn at random from a shuffled pack of 52 cards. Find the probability of drawing a (i) face card and (ii) a card which is neither a king nor a red card.

Explanation:
Total numbers of cards = 52
(i) The number of favourable outcomes of drawing a face card = 12
$\\ \therefore P(E) = \dfrac{12}{52} = \dfrac{3}{13}\\$ (ii) The number of favourable outcomes of drawing neither a king nor a red card
= 52 – (2 + 26)
= 24
$\therefore P(E) = \dfrac{24}{52} = \dfrac{6}{13}\\$

Q5. A bag contains 6 black balls and some white balls. If the probability of drawing a white ball from the bag is double that of a black ball, find the number of white balls in the bag.

Explanation:
Let the number of white balls be x.
Thus, the total number of the possible outcomes
= 6 + x
Now, the favourable outcomes if the black ball is drawn = 6
$\therefore P(B) = \dfrac{6}{6+x}\\$ Again, the favourable outcomes if the white ball is drawn = x
$\therefore P(W) = \dfrac{6}{6+x}\\$ According to the question,
$\dfrac{6}{6+x} = 2\left(\dfrac{6}{6+x}\right)\\$ ⇒ x = 12
Hence, the number of white balls = 12.

CBSE Class 10 Maths Chapter wise Important Questions

Chapter No.	Chapter Name
Chapter 1	Real Numbers
Chapter 2	Polynomials
Chapter 3	Pair of Linear Equations in Two Variable
Chapter 4	Quadratic Equations
Chapter 5	Arithmetic Progressions
Chapter 6	Triangles
Chapter 7	Coordinate Geometry
Chapter 8	Introduction to Trigonometry
Chapter 9	Some Applications of Trigonometry
Chapter 10	Circles
Chapter 11	Areas Related to Circle
Chapter 12	Surface Areas and Volumes
Chapter 13	Statistics
Chapter 14	Probability

Conclusion

To improve your understanding of the Probability chapter, you can explore oswal.io. This platform offers a range of practice questions designed to make learning easier. By practicing these questions, you can strengthen your grasp of probability concepts and enhance your skills in solving probability-related problems.

Chapter Wise Important Questions for CBSE Board Class 10 Maths
Real Numbers
Polynomials
Pair of Linear Equations in Two Variables
Quadratic Equations
Arithmetic Progressions
Triangles
Coordinate Geometry
Introduction to Trigonometry
Some Applications of Trigonometry
Circles
Areas Related to Circles
Surface Areas and Volumes
Statistics
Probability

Class 10 Math Chapter 14
Probability
Important Questions

Introduction

What is probability?

Class 10 Probability Important Questions and Answers

Q1. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will NOT be an ace is :

Options

$(a)\dfrac{1}{13}\\[6.5 bp] (b) \dfrac{1}{4}\\[6.5 bp] (c) \dfrac{12}{13}\\[6.5 bp] (d) \dfrac{3}{4}$

Q2. A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. What is the probability of getting a black ball ?

Options

$(a) \dfrac{2}{5}\\[4.5 bp] \text{(b) }\dfrac{3}{5}\\[4.5 bp] \text{(c) }\dfrac{1}{10}\\[4.5 bp] \text{(d) None of these}$

Q3. A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.

Q4. A card is drawn at random from a shuffled pack of 52 cards. Find the probability of drawing a (i) face card and (ii) a card which is neither a king nor a red card.

Q5. A bag contains 6 black balls and some white balls. If the probability of drawing a white ball from the bag is double that of a black ball, find the number of white balls in the bag.

CBSE Class 10 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1 : How is the probability of an event calculated?

Q2 : What is the sum of the probabilities of all possible outcomes in an experiment?

Q3 : How can you find the probability of an event not occurring?

Q4 : What does a probability of 0.5 represent?

Q5: Define an "event" in probability terms.

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Class 10 Math Chapter 14 Probability Important Questions

Introduction

What is probability?

Class 10 Probability Important Questions and Answers

Q1. A card is drawn from a well-shuffled deck of 52 playing cards. The probability that the card will NOT be an ace is :

Options

(a)\dfrac{1}{13}\\[6.5 bp] (b) \dfrac{1}{4}\\[6.5 bp] (c) \dfrac{12}{13}\\[6.5 bp] (d) \dfrac{3}{4}

Q2. A bag contains 4 red and 6 black balls. A ball is taken out of the bag at random. What is the probability of getting a black ball ?

Options

(a) \dfrac{2}{5}\\[4.5 bp] \text{(b) }\dfrac{3}{5}\\[4.5 bp] \text{(c) }\dfrac{1}{10}\\[4.5 bp] \text{(d) None of these}

Q3. A card is drawn from a well shuffled pack of 52 playing cards. Find the probability that the drawn card is neither a king nor a queen.

Q4. A card is drawn at random from a shuffled pack of 52 cards. Find the probability of drawing a (i) face card and (ii) a card which is neither a king nor a red card.

Q5. A bag contains 6 black balls and some white balls. If the probability of drawing a white ball from the bag is double that of a black ball, find the number of white balls in the bag.

CBSE Class 10 Maths Chapter wise Important Questions

Conclusion

Frequently Asked Questions

Q1 : How is the probability of an event calculated?

Q2 : What is the sum of the probabilities of all possible outcomes in an experiment?

Q3 : How can you find the probability of an event not occurring?

Q4 : What does a probability of 0.5 represent?

Q5: Define an "event" in probability terms.

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Class 10 Math Chapter 14
Probability
Important Questions

$(a)\dfrac{1}{13}\\[6.5 bp] (b) \dfrac{1}{4}\\[6.5 bp] (c) \dfrac{12}{13}\\[6.5 bp] (d) \dfrac{3}{4}$

$(a) \dfrac{2}{5}\\[4.5 bp] \text{(b) }\dfrac{3}{5}\\[4.5 bp] \text{(c) }\dfrac{1}{10}\\[4.5 bp] \text{(d) None of these}$