Question

I et $S$ 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

• A. $1.0146$
• B. $1.2085$
• C. $1.0285$
• D. $1.1521$

Answer 1

Answer: (C)

$n(S)=$ all 5 digit $\mathrm{nos}=9\times 10^4$
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 $\therefore 99995=10003+(n-1)7n=12857$ Numbers divisible by 35 $99995=10010+(P-1)35\Rightarrow P=2572$
$\therefore$ Numbers divisible by 7 but not by 35 are $12857-2572=10285$ $\therefore P=\frac{10285}{90000}\therefore 9P=1.0285$
Ans. (C) [1.0285]