The sample space is S = {1, 2, 3, 4}, Pr({l}) = 0.4, Pr({2}) = 0.4, Pr({3}) = 0.1, Pr({4}) = 0.1, A = {1, 2}, and B = {1, 3}.
Check whether the above event is independent by checking three equations:
Pr(A) = Pr(A | B) A is independent of B
Pr(B) = Pr(B | A) B is independent of A
Pr(A n B) = Pr(A)Pr(B). The multiplication rule
Do you ever find a case where only one or two of these equations is satisfied?