NCERT solution Class 11 probability

NCERT Solutions

Class 11 Maths

Probability

NCERT Questions

Ex.16.1 Q.1
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Ex.16.2 Q.1
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Ex.16.3 Q.1
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Misc.Q.1
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Ex.Misc.Q.9
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Ex.15.1 Q.2

Ex.Misc.Q.9

If 4-digit numbers greater than 5,000 are randomly formed from the digits 0, 1, 3, 5, and 7,

what is the probability of forming a number divisible by 5 when,

(1) the digits are repeated?

(2) the repetition of digits is not allowed?

(1) When the digits are repeated

Since four-digit numbers greater than 5000 are formed, the leftmost digit is either 7 or 5.

The remaining 3 places can be filled by any of the digits 0, 1, 3, 5, or 7 as repetition of digits is allowed.

So, total number of 4-digit numbers greater than 5000 = 2 × 5 × 5 × 5 − 1

= 250 − 1 = 249

[In this case, 5000 cannot be counted; so, 1 is subtracted]

A number is divisible by 5 if the digit at its units place is either 0 or 5.

So, total number of 4-digit numbers greater than 5000 that are divisible by 5 = 2 × 5 × 5 × 2 − 1

= 100 − 1 = 99

Thus, the probability of forming a number divisible by 5 when the digits are repeated = =

(2) When repetition of digits is not allowed

The thousands place can be filled with either of the two digits 5 or 7.

The remaining 3 places can be filled with any of the remaining 4 digits.

Total number of 4-digit numbers greater than 5000 = 2 × 4 × 3 × 2 = 48

When the digit at the thousands place is 5, the units place can be

filled only with 0 and the tens and hundreds of places can be filled with any two of the remaining 3 digits.

Here, number of 4-digit numbers starting with 5 and divisible by 5 = 3 × 2 = 6

When the digit at the thousands place is 7, the units place can be filled in two ways (0 or 5) and

the tens and hundreds of places can be filled with any two of the remaining 3 digits.

Here, number of 4-digit numbers starting with 7 and divisible by 5 = 1 × 2 × 3 × 2 = 12

So, total number of 4-digit numbers greater than 5000 that are divisible by 5

= 6 + 12 = 18

Thus, the probability of forming a number divisible by 5 when the repetition of digits is not allowed = =

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.
Match with Our Solution: After attempting the question, compare your result and approach with the provided NCERT solution. This step allows you to identify any mistakes or gaps in your understanding.
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.
Review and Revise: Regularly review the concepts and solutions you've learned. Revise your notes and practice regularly to retain the knowledge effectively. You may refer Probability Class 11 Maths Notes.
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NCERT solutions of Probability Class 11 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 11 Maths Probability NCERT solutions.