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From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18?
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From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. F...
Probability of drawing a multiple of 12 and 18:
To find the probability of drawing a number that is a multiple of both 12 and 18, we need to find the number of multiples of the least common multiple (LCM) of 12 and 18, which is 36, in the given range of numbers (1 to 1000).
Step 1: Finding the number of multiples of 36 in the given range
The first multiple of 36 in the given range is 36 itself. The last multiple of 36 in the given range is 1008, which is beyond the range. Therefore, we need to find the number of multiples of 36 from 36 to 1000.
Number of multiples of 36 = (1000 - 36)/36 + 1 = 28
Step 2: Calculating the probability
The total number of numbers in the given range is 1000.
Probability of drawing a multiple of 12 and 18 = Number of multiples of 36 / Total number of numbers in the range = 28/1000
Probability of drawing a multiple of 12 and 18 = 0.028
Probability of drawing a multiple of 12 or 18:
To find the probability of drawing a number that is a multiple of either 12 or 18, we need to find the number of multiples of 12 and 18 in the given range and then subtract the number of multiples of their LCM to avoid double counting.
Step 1: Finding the number of multiples of 12 and 18 in the given range
Number of multiples of 12 = (1000/12) = 83.33 (rounded down to 83)
Number of multiples of 18 = (1000/18) = 55.56 (rounded down to 55)
Step 2: Finding the number of multiples of their LCM (36)
Number of multiples of 36 = (1000/36) = 27.78 (rounded down to 27)
Step 3: Calculating the probability
The total number of numbers in the given range is 1000.
Probability of drawing a multiple of 12 or 18 = (Number of multiples of 12 + Number of multiples of 18 - Number of multiples of 36) / Total number of numbers in the range
= (83 + 55 - 27) / 1000
Probability of drawing a multiple of 12 or 18 = 0.111
Therefore, the probability of drawing a number that is a multiple of 12 and 18 is 0.028, and the probability of drawing a number that is a multiple of either 12 or 18 is 0.111.
To find the probability of drawing a number that is a multiple of both 12 and 18, we need to find the number of multiples of the least common multiple (LCM) of 12 and 18, which is 36, in the given range of numbers (1 to 1000).
Step 1: Finding the number of multiples of 36 in the given range
The first multiple of 36 in the given range is 36 itself. The last multiple of 36 in the given range is 1008, which is beyond the range. Therefore, we need to find the number of multiples of 36 from 36 to 1000.
Number of multiples of 36 = (1000 - 36)/36 + 1 = 28
Step 2: Calculating the probability
The total number of numbers in the given range is 1000.
Probability of drawing a multiple of 12 and 18 = Number of multiples of 36 / Total number of numbers in the range = 28/1000
Probability of drawing a multiple of 12 and 18 = 0.028
Probability of drawing a multiple of 12 or 18:
To find the probability of drawing a number that is a multiple of either 12 or 18, we need to find the number of multiples of 12 and 18 in the given range and then subtract the number of multiples of their LCM to avoid double counting.
Step 1: Finding the number of multiples of 12 and 18 in the given range
Number of multiples of 12 = (1000/12) = 83.33 (rounded down to 83)
Number of multiples of 18 = (1000/18) = 55.56 (rounded down to 55)
Step 2: Finding the number of multiples of their LCM (36)
Number of multiples of 36 = (1000/36) = 27.78 (rounded down to 27)
Step 3: Calculating the probability
The total number of numbers in the given range is 1000.
Probability of drawing a multiple of 12 or 18 = (Number of multiples of 12 + Number of multiples of 18 - Number of multiples of 36) / Total number of numbers in the range
= (83 + 55 - 27) / 1000
Probability of drawing a multiple of 12 or 18 = 0.111
Therefore, the probability of drawing a number that is a multiple of 12 and 18 is 0.028, and the probability of drawing a number that is a multiple of either 12 or 18 is 0.111.
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From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18?
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From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18? for Engineering Mathematics 2024 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18? covers all topics & solutions for Engineering Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18?.
From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18? for Engineering Mathematics 2024 is part of Engineering Mathematics preparation. The Question and answers have been prepared according to the Engineering Mathematics exam syllabus. Information about From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18? covers all topics & solutions for Engineering Mathematics 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for From the numbers 1,2,3,4……… 999,1000 one numbers is drawn at random. Find the probability that the number is multiple of i) 12 and 18, ii) 12 or 18?.
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