Question

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

• A. $\frac{73}{500}$
• B. $\frac{71}{1000}$
• C. $\frac{143}{1000}$
• D. $\frac{71}{500}$

Answer 1

Answer: (D)

Total number of numbers from 2 to $1001=1000$
Now, the numbers, which leaves remainder 1 when divided by 7, are $8,15,22,\dots ,995.$
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
$=\frac{142}{1000}=\frac{71}{500}$