1. Tardigrade
  2. Question
  3. Mathematics
  4. 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 9 p is equal to

Question Error Report

Thank you for reporting, we will resolve it shortly

Back to Question

Q. 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 $9 p$ is equal to

JEE MainJEE Main 2022Probability - Part 2

Solution:

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