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  4. A number n is chosen at random from the natural numbers 2 to 1001 . The probability that n is a number that leaves remainder 1 when divided by 7 , is

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Q. A number $n$ is chosen at random from the natural numbers $2$ to $1001$ . The probability that $n$ is a number that leaves remainder $1$ when divided by $7$ , is

TS EAMCET 2018

Solution:

Total number of numbers from 2 to $1001=1000$
Now, the numbers, which leaves remainder 1 when divided by 7, are $8,15,22, \ldots, 995 .$
Let these are $m$ in counting, then we have
$995=8+(m-1) 7 \Rightarrow 987=(m-1) 7$
$\Rightarrow m-1=141 \Rightarrow m=142$
$\therefore $ Required probability
$=\frac{142}{1000}=\frac{71}{500}$