Let S be the sample space of all five digit numbers.

Question

Let $S$ be the sample space of all five digit numbers. It $p$ 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 :

Accepted Answer

Among the 5 digit numbers,

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

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

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

$= 12857$

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

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

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

$= 2572$

Hence number of number divisible by 7 but not by 5

$= 12857 - 2572$

$= 10285$

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

$= 1.0285$

Solutions · 1