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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?
- a)0.25
- b)0.32
- c)0.22
- d)0.33
Correct answer is option 'C'. Can you explain this answer?
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Most Upvoted Answer
A number is selected at random from the first 1000 natural numbers. Wh...
Solution:
Total Number of Natural Numbers from 1 to 1000 = 1000
Total number of multiples of 7 from 1 to 1000 = 142
Total number of multiples of 11 from 1 to 1000 = 90
Total number of common multiples of 7 and 11 from 1 to 1000 = 63
Therefore, the total number of numbers that are multiple of 7 or 11 = 142 + 90 - 63 = 169
Probability of selecting a number that is multiple of 7 or 11 = 169/1000
= 0.169
= 0.22 (approx.)
Hence, the correct option is (C) 0.22.
Total Number of Natural Numbers from 1 to 1000 = 1000
Total number of multiples of 7 from 1 to 1000 = 142
Total number of multiples of 11 from 1 to 1000 = 90
Total number of common multiples of 7 and 11 from 1 to 1000 = 63
Therefore, the total number of numbers that are multiple of 7 or 11 = 142 + 90 - 63 = 169
Probability of selecting a number that is multiple of 7 or 11 = 169/1000
= 0.169
= 0.22 (approx.)
Hence, the correct option is (C) 0.22.
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Community Answer
A number is selected at random from the first 1000 natural numbers. Wh...
A=Multiple of 7
B=Multiple of 11
A=1000÷7=142
->1000= 142×7 +6
B=1000÷11=90
->1000= 90×11 +10
LCM of 7 and 11 is 77
1000÷77=12
->1000= 12×77 +76
P(A)=142÷1000
P(B)=90÷1000
P(A intersection B)=12÷1000
P(AUB) = P(A) + P(B) - P(A intersection B)
= 142÷1000 + 90÷1000 - 12÷1000
= 0.22
B=Multiple of 11
A=1000÷7=142
->1000= 142×7 +6
B=1000÷11=90
->1000= 90×11 +10
LCM of 7 and 11 is 77
1000÷77=12
->1000= 12×77 +76
P(A)=142÷1000
P(B)=90÷1000
P(A intersection B)=12÷1000
P(AUB) = P(A) + P(B) - P(A intersection B)
= 142÷1000 + 90÷1000 - 12÷1000
= 0.22
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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?a)0.25b)0.32c)0.22d)0.33Correct answer is option 'C'. Can you explain this answer?
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