JEE Main 2022 — Probability Question with Solution

Among the 5 digit numbers,

First number divisible by 7 is 10003 and last is 99995.

$$\Rightarrow$$ Number of numbers divisible by 7.

$$=\frac{99995-10003}{7}+1$$

$$=12857$$

First number divisible by 35 is 10010 and last is 99995.

$$\Rightarrow$$ Number of numbers divisible by 35

$$=\frac{99995-10010}{35}+1$$

$$=2572$$

Hence number of number divisible by 7 but not by 5

$$=12857-2572$$

$$=10285$$

$$9P.=\frac{10285}{90000}\times 9$$

$$=1.0285$$