Question: The sample space is S = {1, 2, 3, 4}, Pr({1}) = 0.48, Pr({2}) = 0.12, Pr({3}) = 0.32, Pr({4}) = 0.08, A = {3,

The sample space is S = {1, 2, 3, 4}, Pr({1}) = 0.48, Pr({2}) = 0.12, Pr({3}) = 0.32, Pr({4}) = 0.08, A = {3, 4), 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?

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