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Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33?
selected would be a multiple of 7 or 11?
(a) 0.25 (b) 0.32 (c) 0.22 (d) 0.33?
Most Upvoted Answer
Q.10. A number is selected at random from the first 1000 natural numbe...
Calculating the Probability of Selecting a Multiple of 7 or 11
To calculate the probability of selecting a number that is a multiple of 7 or 11 from the first 1000 natural numbers, we first need to determine the total number of multiples of 7 and 11 within this range.
Finding the Number of Multiples of 7
There are 1000 ÷ 7 = 142 multiples of 7 within the first 1000 natural numbers.
Finding the Number of Multiples of 11
Similarly, there are 1000 ÷ 11 = 90 multiples of 11 within this range.
Finding the Number of Multiples of 7 and 11
To find the number of numbers that are multiples of both 7 and 11, we need to find the least common multiple (LCM) of 7 and 11, which is 77. There are 1000 ÷ 77 = 12 numbers that are multiples of both 7 and 11.
Calculating the Total Number of Multiples of 7 or 11
Now, we need to add the number of multiples of 7, multiples of 11, and subtract the multiples of both 7 and 11 to avoid double counting.
Total = 142 + 90 - 12 = 220
Calculating the Probability
The probability of selecting a number that is a multiple of 7 or 11 is given by:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 220 / 1000
Probability = 0.22
Therefore, the correct answer is (c) 0.22.
To calculate the probability of selecting a number that is a multiple of 7 or 11 from the first 1000 natural numbers, we first need to determine the total number of multiples of 7 and 11 within this range.
Finding the Number of Multiples of 7
There are 1000 ÷ 7 = 142 multiples of 7 within the first 1000 natural numbers.
Finding the Number of Multiples of 11
Similarly, there are 1000 ÷ 11 = 90 multiples of 11 within this range.
Finding the Number of Multiples of 7 and 11
To find the number of numbers that are multiples of both 7 and 11, we need to find the least common multiple (LCM) of 7 and 11, which is 77. There are 1000 ÷ 77 = 12 numbers that are multiples of both 7 and 11.
Calculating the Total Number of Multiples of 7 or 11
Now, we need to add the number of multiples of 7, multiples of 11, and subtract the multiples of both 7 and 11 to avoid double counting.
Total = 142 + 90 - 12 = 220
Calculating the Probability
The probability of selecting a number that is a multiple of 7 or 11 is given by:
Probability = Number of favorable outcomes / Total number of outcomes
Probability = 220 / 1000
Probability = 0.22
Therefore, the correct answer is (c) 0.22.
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Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33?
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Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33?.
Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33? for UPSC 2024 is part of UPSC preparation. The Question and answers have been prepared according to the UPSC exam syllabus. Information about Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33? covers all topics & solutions for UPSC 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33?.
Solutions for Q.10. 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) 0.25 (b) 0.32 (c) 0.22 (d) 0.33? in English & in Hindi are available as part of our courses for UPSC.
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