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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, $$P(A)=\left\lfloor\dfrac {1000}7\right\rfloor\approx 142$$
Number of multiples of $$11$$ in first $$1000$$ natural numbers, $$P(B)=\left\lfloor\dfrac {1000}{11}\right\rfloor\approx 90$$
And, numbers divisible by $$7$$ and $$11$$ are $$P(A\cap B)=\left\lfloor\dfrac {1000}{11\times 7}\right\rfloor\approx  12$$
Hence the probability that the number so selected would be a multiple of $$7$$ or $$11$$ 
$$=P(A)+P(B)-P(A\cap B)=\dfrac {142}{1000}+\dfrac {90}{1000}-\dfrac {12}{1000}=\dfrac {142+90-12}{1000}=0.22$$

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