Probability Part 2

S={1,2,3,.........2022}
HCF(n,2022)=1
⇒n and 2022 have no common factor
Total elements =2022
2022=2×3×337
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∪N)=n(M)+n(N)−n(L)
=1011+674−337
=1348
0= Number divisible by 337 but not in M∪N
{337,1685}
Number divisible by 2,3 or 337
=1348+2=1350
Required probability =‌

2022−1350

2022

=‌

672

2022

=‌

112

337