UPSC Exam > UPSC Questions > . A number is selected at random from the fir...
Start Learning for Free
. A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?
Most Upvoted Answer
. A number is selected at random from the first 1000 natural numbers. ...
Understanding the Problem
To find the probability of selecting a number from the first 1000 natural numbers that is a multiple of 7 or 11, we can use the principle of inclusion-exclusion.
Step 1: Identify Multiples of 7
- The multiples of 7 up to 1000 are given by:
- 7, 14, 21, ..., 994.
- To find how many multiples there are, we calculate:
- Last multiple = 7 * 142 = 994.
- Thus, there are 142 multiples of 7.
Step 2: Identify Multiples of 11
- The multiples of 11 up to 1000 are:
- 11, 22, 33, ..., 990.
- To find how many multiples there are:
- Last multiple = 11 * 90 = 990.
- Thus, there are 90 multiples of 11.
Step 3: Identify Common Multiples (Multiples of 77)
- The least common multiple of 7 and 11 is 77.
- The multiples of 77 up to 1000 are:
- 77, 154, 231, ..., 924.
- To find how many multiples there are:
- Last multiple = 77 * 12 = 924.
- Thus, there are 12 multiples of 77.
Step 4: Apply Inclusion-Exclusion Principle
- Total multiples of 7 or 11:
- Total = (Multiples of 7) + (Multiples of 11) - (Common multiples)
- Total = 142 + 90 - 12 = 220.
Step 5: Calculate Probability
- The total number of natural numbers from 1 to 1000 is 1000.
- Probability = (Total multiples of 7 or 11) / (Total numbers)
- Probability = 220 / 1000 = 0.22.
Conclusion
The probability that a randomly selected number from the first 1000 natural numbers is a multiple of 7 or 11 is 0.22 or 22%.
To find the probability of selecting a number from the first 1000 natural numbers that is a multiple of 7 or 11, we can use the principle of inclusion-exclusion.
Step 1: Identify Multiples of 7
- The multiples of 7 up to 1000 are given by:
- 7, 14, 21, ..., 994.
- To find how many multiples there are, we calculate:
- Last multiple = 7 * 142 = 994.
- Thus, there are 142 multiples of 7.
Step 2: Identify Multiples of 11
- The multiples of 11 up to 1000 are:
- 11, 22, 33, ..., 990.
- To find how many multiples there are:
- Last multiple = 11 * 90 = 990.
- Thus, there are 90 multiples of 11.
Step 3: Identify Common Multiples (Multiples of 77)
- The least common multiple of 7 and 11 is 77.
- The multiples of 77 up to 1000 are:
- 77, 154, 231, ..., 924.
- To find how many multiples there are:
- Last multiple = 77 * 12 = 924.
- Thus, there are 12 multiples of 77.
Step 4: Apply Inclusion-Exclusion Principle
- Total multiples of 7 or 11:
- Total = (Multiples of 7) + (Multiples of 11) - (Common multiples)
- Total = 142 + 90 - 12 = 220.
Step 5: Calculate Probability
- The total number of natural numbers from 1 to 1000 is 1000.
- Probability = (Total multiples of 7 or 11) / (Total numbers)
- Probability = 220 / 1000 = 0.22.
Conclusion
The probability that a randomly selected number from the first 1000 natural numbers is a multiple of 7 or 11 is 0.22 or 22%.
Attention UPSC Students!
To make sure you are not studying endlessly, EduRev has designed UPSC study material, with Structured Courses, Videos, & Test Series. Plus get personalized analysis, doubt solving and improvement plans to achieve a great score in UPSC.
|
Explore Courses for UPSC exam
|
|
Top Courses for UPSCView all
. A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?
Question Description
. A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?.
. A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?.
Solutions for . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? in English & in Hindi are available as part of our courses for UPSC.
Download more important topics, notes, lectures and mock test series for UPSC Exam by signing up for free.
Here you can find the meaning of . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? defined & explained in the simplest way possible. Besides giving the explanation of
. A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?, a detailed solution for . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? has been provided alongside types of . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? theory, EduRev gives you an
ample number of questions to practice . A number is selected at random from the first 1000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11? tests, examples and also practice UPSC tests.
|
|
Explore Courses for UPSC exam
|
|
Signup for Free!
Signup to see your scores go up within 7 days! Learn & Practice with 1000+ FREE Notes, Videos & Tests.
|
© EduRev
|
Education Revolution
|
Follow Us
|
Signup to see your scores
go up within 7 days!
Access 1000+ FREE Docs, Videos and Tests
Takes less than 10 seconds to signup