JEE MAIN - Mathematics (2022 - 27th July Morning Shift - No. 12)
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 :
1.0146
1.2085
1.0285
1.1521
Explanation
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
$$ = 12857 - 2572$$
$$ = 10285$$
$$9P. = {{10285} \over {90000}} \times 9$$
$$ = 1.0285$$
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