Problem 5. Let E, F, G be events in a probability space with sample space S and probability law Pr(), which satisfy Pr(EFG) Pr(EFG) = Pr(EFG) = Pr(EFG) = 1,4 Pr(EFG) Pr(EFG) = Pr(EFG) = Pr(EFG) = 0. Prove the following statements. (a) Show that the above conditions are valid by showing that the above events are mutually exclusive and their union is S. (b) E and F are independent. (c) E and G are independent. (d) F and G are independent. (e) E, F, G are not independent.