A number  $n$ is chosen at random from $\left\{1,2,3,4,...........1000\right\}.$the probability that n is a number that leaves remainder 1 when divided by 7 is

Let A be the set of all numbers from $\{1,2,3\dots \dots \dots .,1000\}$ that leave remainder 1 when divided by 7.
$\begin{array}{l}\therefore \mathrm{A}=\{1,8,15,22,\dots \dots ,995\}\Rightarrow \mathrm{n}\left(\mathrm{A}\right)=\frac{995-1}{7}+1=142+1=143\\ \therefore \mathrm{P}\left(\mathrm{A}\right)=\frac{143}{1000}\end{array}$