NCERT solution Class 11 probability

NCERT Solutions

Class 11 Maths

Probability

NCERT Questions

Ex.16.1 Q.1
Ex.16.1 Q.2
Ex.16.1 Q.3
Ex.16.1 Q.4
Ex.16.1 Q.5
Ex.16.1 Q.6
Ex.16.1 Q.7
Ex.16.1 Q.8
Ex.16.1 Q.9
Ex.16.1 Q.10
Ex.16.1 Q.11
Ex.16.1 Q.12
Ex.16.1 Q.13
Ex.16.1 Q.14
Ex.16.1 Q.15
Ex.16.1 Q.16
Ex.16.2 Q.1
Ex.16.2 Q.2
Ex.16.2 Q.3
Ex.16.2 Q.4
Ex.16.2 Q.5
Ex.16.2 Q.6
Ex.16.2 Q.7
Ex.16.3 Q.1
Ex.16.3 Q.2
Ex.16.3 Q.3
Ex.16.3 Q.4
Ex.16.3 Q.3
Ex.16.3 Q.6
Ex.16.3 Q.7
Ex.16.3 Q.8
Ex.16.3 Q.9
Ex.16.3 Q.10
Ex.16.3 Q.11
Ex.16.3 Q.12
Ex.16.3 Q.13
Ex.16.3 Q.14
Ex.16.3 Q.15
Ex.16.3 Q.16
Ex.16.3 Q.17
Ex.16.3 Q.18
Ex.16.3 Q.19
Ex.16.3 Q.20
Ex.16.3 Q.21
Misc.Q.1
Ex.Misc.Q.2
Ex.Misc.Q.3
Ex.Misc.Q.4
Ex.Misc.Q.5
Ex.Misc.Q.6
Ex.Misc.Q.7
Ex.Misc.Q.8
Ex.Misc.Q.9
Ex.Misc.Q.10
Ex.15.1 Q.2

Ex.16.2 Q.6

Two dice are thrown. The events A, B and C are as follows:

A: getting an even number on the first die.

B: getting an odd number on the first die.

C: getting the sum of the numbers on the dice ≤ 5.

Describe the events

(1) A′

(2) not B

(3) A or B

(4) A and B

(5) A but not C

(6) B or C

(7) B and C

(8) A ∩ B′ ∩ C′

When a pair of dice is rolled, the sample space is given by:

S = {(x, y): x comes from 1^st dice and y comes from 2^nd dice and x, y = 1, 2, 3, 4, 5, 6}

= {(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)}

Now, A: getting an even number on the first die.

A = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4),

(4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

B: getting an odd number on the first die.

B = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5),

(3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}

C: getting the sum of the numbers on the dice ≤ 5

C = {(1, 1), (1, 2), (1, 3), (1, 4), (2, 1), (2, 2), (2, 3), (3, 1), (3, 2), (4, 1)}

Now,

(1) A’ = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (3, 1), (3, 2), (3, 3), (3, 4), (3, 5),

(3, 6), (5, 1), (5, 2), (5, 3), (5, 4), (5, 5), (5, 6)}

(2) Not B = B’ = {(2, 1), (2, 2), (2, 3), (2, 4), (2, 5), (2, 6), (4, 1), (4, 2), (4, 3), (4, 4),

(4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)} = A

(3) A or B = A U B

= {(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)

= S

(4) A and B = A ∩ B = ф

(5) A but not C = A – C = {(2, 4), (2, 5), (2, 6), (4, 2), (4, 3), (4, 4), (4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

(6) B or C = B U C = {(1, 1), (1, 2), (1, 3), (1, 4), (1, 5), (1, 6), (2, 1), (2, 2), (2, 3), (3, 1),

(3, 2), (3, 3), (3, 4), (3, 5), (3, 6), (4, 1), (5, 1), (5, 2) , (5, 3), (5, 4), (5, 5), (5, 6)}

(7) B and C = B ∩ C = {(1, 1), (1, 2), (1, 3), (1, 4), (3, 1), (3, 2)}

(8) C’ = {(1, 5), (1, 5), (2, 4), (2, 5), (2, 6), (3, 3), (3, 4), (3, 5), (3, 6), (4, 2), (4, 3), (4, 4),

(4, 5), (4, 6), (5, 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)}

So, A ∩ B’ ∩ C’ = A ∩ A ∩ C’ = A ∩ C’ = {(2, 4), (2, 5), (2, 6), (4, 2), (4, 3), (4, 4),

(4, 5), (4, 6), (6, 1), (6, 2), (6, 3), (6, 4), (6, 5), (6, 6)}

Probability Class 11 Maths NCERT Chapter 14 NCERT Solutions

Solving NCERT textbook questions of Probability Class 11 Maths NCERT Chapter 14 is a crucial step to gauge your understanding of the concepts. It provides you with an opportunity to assess your grasp of the material after learning each chapter. We have already provided solutions to all the exercises in the NCERT textbook of Class 11 Maths Probability, available in various formats such as video, text, and downloadable PDFs. If you need assistance with any of the NCERT questions or any other academic topics, feel free to ask in the “Ask Questions” section of LearnoHub.com.

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Using the NCERT solutions module effectively can significantly enhance your learning experience and understanding of the subject matter. Here's a step-by-step guide on how to make the most out of the NCERT solutions:

Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Probability Class 11 Maths NCERT Chapter 14 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 11 Maths Probability Online Test on LearnoHub.com.
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