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 =