Correct option is (D) 112/337
Total number of elements = 2022
2022 = 2 × 3 × 337
HCF (n, 2022) = 1
is feasible when the value of 'n' and 2022 has no common factor.
A = Number which are divisible by 2 from {1,2,3.....2022}
n(A) = 1011
B = Number which are divisible by 3 by 3
from {1,2,3......2022}
n(B) = 674
A∩B = Number which are divisible by 6
from {1,2,3........2022}
6,12,18........., 2022
337 = n (A ∩ B)
n(AUB) = n(A) + n(B) – n(AIB)
= 1011+ 674 –337
= 1348
C= Number which divisible by 337 from
{1,........1022}
Total elements which are divisible by 2 or 3 or 337
= 1348 +2 = 1350
Favourable cases = Element which are neither
divisible by 2, 3 or 337
= 2022 – 1350
= 672
Required probability = 672/2022 = 112/337
