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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?
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A number is selected at random from the first 1000 natural numbers. Wh...
Probability of selecting a multiple of 7 or 11 from the first 1000 natural numbers
To solve this problem, we need to first find out how many numbers from 1 to 1000 are multiples of 7 or 11.
Finding the number of multiples of 7 or 11 in the first 1000 natural numbers
Multiples of 7: There are 142 multiples of 7 in the first 1000 natural numbers. This can be found by dividing 1000 by 7, which gives 142 with a remainder of 6. Therefore, there are 142 multiples of 7 in the first 1000 natural numbers.
Multiples of 11: There are 90 multiples of 11 in the first 1000 natural numbers. This can be found by dividing 1000 by 11, which gives 90 with a remainder of 10. Therefore, there are 90 multiples of 11 in the first 1000 natural numbers.
Finding the number of common multiples of 7 and 11 in the first 1000 natural numbers
Multiples of 7 and 11: To find the number of common multiples of 7 and 11 in the first 1000 natural numbers, we need to find the multiples of their LCM (Least Common Multiple), which is 77. There are 12 multiples of 77 in the first 1000 natural numbers. This can be found by dividing 1000 by 77, which gives 12 with a remainder of 44. Therefore, there are 12 common multiples of 7 and 11 in the first 1000 natural numbers.
Calculating the probability of selecting a multiple of 7 or 11 from the first 1000 natural numbers
Now that we know the number of multiples of 7 or 11 and the number of common multiples of 7 and 11 in the first 1000 natural numbers, we can calculate the probability of selecting a multiple of 7 or 11.
Probability = (Number of multiples of 7 or 11)/(Total number of natural numbers from 1 to 1000)
Total number of natural numbers from 1 to 1000 = 1000
Number of multiples of 7 or 11 = (142 + 90) - 12 = 220
Therefore, Probability = 220/1000 = 0.22 or 22%
Conclusion
The probability of selecting a multiple of 7 or 11 from the first 1000 natural numbers is 0.22 or 22%.
To solve this problem, we need to first find out how many numbers from 1 to 1000 are multiples of 7 or 11.
Finding the number of multiples of 7 or 11 in the first 1000 natural numbers
Multiples of 7: There are 142 multiples of 7 in the first 1000 natural numbers. This can be found by dividing 1000 by 7, which gives 142 with a remainder of 6. Therefore, there are 142 multiples of 7 in the first 1000 natural numbers.
Multiples of 11: There are 90 multiples of 11 in the first 1000 natural numbers. This can be found by dividing 1000 by 11, which gives 90 with a remainder of 10. Therefore, there are 90 multiples of 11 in the first 1000 natural numbers.
Finding the number of common multiples of 7 and 11 in the first 1000 natural numbers
Multiples of 7 and 11: To find the number of common multiples of 7 and 11 in the first 1000 natural numbers, we need to find the multiples of their LCM (Least Common Multiple), which is 77. There are 12 multiples of 77 in the first 1000 natural numbers. This can be found by dividing 1000 by 77, which gives 12 with a remainder of 44. Therefore, there are 12 common multiples of 7 and 11 in the first 1000 natural numbers.
Calculating the probability of selecting a multiple of 7 or 11 from the first 1000 natural numbers
Now that we know the number of multiples of 7 or 11 and the number of common multiples of 7 and 11 in the first 1000 natural numbers, we can calculate the probability of selecting a multiple of 7 or 11.
Probability = (Number of multiples of 7 or 11)/(Total number of natural numbers from 1 to 1000)
Total number of natural numbers from 1 to 1000 = 1000
Number of multiples of 7 or 11 = (142 + 90) - 12 = 220
Therefore, Probability = 220/1000 = 0.22 or 22%
Conclusion
The probability of selecting a multiple of 7 or 11 from the first 1000 natural numbers is 0.22 or 22%.
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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?
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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 CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation 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 CA Foundation 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 CA Foundation 2024 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation 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 CA Foundation 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?.
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