JEE Main 2022 — Probability Question with Solution

Given, five-digit number,

So $n\left(S\right)=$total $5$ digit number will be$=9\times {10}^4$

Now let $A:$ number is multiple of $7$ but not divisible by $5$

Smallest $5$ digit divisible by $7$ is $10003$

Largest $5$ digit divisible by $7$ is $99995$

Now by using $n^{th}$ term of A.P formula we have,

$\therefore 99995=10003+\left(n-1\right)7$

$\Rightarrow n=12857$

Now finding number which is divisible by $35$

Again using A.P formula we have,

$99995=10010+\left(P-1\right)35$

$\Rightarrow P=2572$

Now number divisible by $7$ but not by $35$ are

$12857-2572=10285$

So, probability will be $P=\frac{10285}{90000}$

And $9P=1.0285$