A number is selected at random from the first 1,000 natural numbers. What is the probability that the number so selected would be a multiple of 7 or 11?
A
0.25
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B
0.32
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C
0.22
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D
0.33
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Solution
The correct option is C0.22 Given: First 1000 natural numbers
To find: the probability that the number so selected would be a multiple of 7 or 11
Sol: According to the question, n(S)=1000
Number of multiples of 7 in first 1000 natural numbers, P(A)=⌊10007⌋≈142
Number of multiples of 11 in first 1000 natural numbers, P(B)=⌊100011⌋≈90
And, numbers divisible by 7 and 11 are P(A∩B)=⌊100011×7⌋≈12
Hence the probability that the number so selected would be a multiple of 7 or 11