A number n is chosen at random from the natur | vedclass

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(D) The total number of natural numbers from $2$ to $1001$ is $1001 - 2 + 1 = 1000$.We are looking for numbers $n$ such that $n \equiv 1 \pmod{7}$.The

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$\frac{71}{500}$

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(D) The total number of natural numbers from $2$ to $1001$ is $1001 - 2 + 1 = 1000$.We are looking for numbers $n$ such that $n \equiv 1 \pmod{7}$.The sequence of such numbers starting from $2$ is $8, 15, 22, \dots, 995$.This is an arithmetic progression where the first term $a = 8$, the common difference $d = 7$, and the last term $l = 995$.Using the formula $l = a + (m - 1)d$, we have:$995 = 8 + (m - 1)7$$987 = (m - 1)7$$m - 1 = 141$$m = 142$.The required probability is $\frac{m}{	ext{Total numbers}} = \frac{142}{1000} = \frac{71}{500}$.

$A$ 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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