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Question

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 C 0.22
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)=10007142
Number of multiples of 11 in first 1000 natural numbers, P(B)=10001190
And, numbers divisible by 7 and 11 are P(AB)=100011×712
Hence the probability that the number so selected would be a multiple of 7 or 11
=P(A)+P(B)P(AB)=1421000+901000121000=142+90121000=0.22

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