QJEEM22Ma7c5a: JEE Main 2022 Mathematics - Class 12 JEEM22Ma7c5a Solution: Let . Then the probability, that a randomly chosen number n…

S = {1, 2, 3, .......... 2022}

HCF (n, 2022) = 1

$\Rightarrow$ n and 2022 have no common factor

Total elements = 2022

2022 = 2 $\times$ 3 $\times$ 337

M : numbers divisible by 2.

{2, 4, 6, ........, 2022} $\,\,\,\,$ n(M) = 1011

N : numbers divisible by 3.

{3, 6, 9, ........, 2022} $\,\,\,\,$ n(N) = 674

L : numbers divisible by 6.

{6, 12, 18, ........, 2022} $\,\,\,\,$ n(L) = 337

n(M $\cup$ N) = n(M) + n(N) $-$ n(L)

= 1011 + 674 $-$ 337

= 1348

0 = Number divisible by 337 but not in M $\cup$ N

{337, 1685}

Number divisible by 2, 3 or 337

= 1348 + 2 = 1350

Required probability $= {{2022 - 1350} \over {2022}}$

$= {{672} \over {2022}}$

$= {{112} \over {337}}$