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Let $\mathrm{ S}$ be the sample space of all five digit numbers. It $\mathrm{ p}$ is the probability that a randomly selected number from $\mathrm{ S}$ , is a multiple of $\mathrm{ 7}$ but not divisible by $\mathrm{ 5}$ , then $\mathrm{ 9 p}$ is equal to
Option: 1
$1.0146$

Option: 2
$1.2085$

Option: 3
$1.0285$

Option: 4
$1.1521$

Answers (1)

best_answer

$\mathrm{n(s)=\text { all } 5 \text { digit nos }=9 \times 10^{4}}$

A: no is multiple of 7 but not divisible by 5

Smallest 5 digit divisible by 7 is $1003$

Largest 5 digit divisible by 7 is $99995$

$\therefore 99995=10003+(n-1) 7 \Rightarrow n=12857$

Numbers divisible by 35

$\mathrm{99995=10010+(P-1) 35 \Rightarrow P=2572}$

$\therefore$ Numbers divisible by 7 but not by 35 are

$12857-2572=10285 \\$

$\mathrm{\therefore \quad P=\frac{10285}{90000} \qquad \because 9 P=1.0285 }$

Hence correct option is 3

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Gaurav

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