Let S be the sample space of all five digit numbers. If p is the probability that a randomly selected number from S, is a multiple of 7 but not divisible by 5, then 9p is equal to

n(S) = all 5 digit nos = 9 × 10⁴

A : no 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

$\therefore$ 99995 = 10003 + (n – 1) 7

$\therefore$ Numbers  divisible by5= n = 12857

Numbers divisible by 35

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

$\therefore$ Numbers  divisible by7 but not by 35 are

            12857 – 2572 = 10285

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

Ans. (C) [1.0285]