P(A)=0.64,P(B)=0.45,P(B∪A)=0.92 Find the following probabilities. P(A∩B) =  P(B|A¯) =  P(A¯|B) =

For each set of probabilities, determine whether the events A and B are independent or dependent. (If necessary, consult a list of formulas.) Probabilities Independent Dependent = P(A 18) - 1 (a) P(A)=-;P(B) =;P(A\B) = 5 1 1 P(A) =;P (B) = P(A and B) = %3D 4 6. 1 1 P (B|A) = 1 (c) P(4)-극: P(B)-P(Bl4): %3D %3D 1 1 (d) P(A) = : P(B) = P(4 |B) = | %3D

Possible values of X, the number of components in a system submitted for repair that must be replaced, are 1, 2, 3, and 4 with corresponding probabilities 0.45, 0.05, 0.45, and 0.05, respectively. (0) Calculate E(X) and then E(5 - X). E(X) - E(5 - X) - 150 (b) Would the repair facility be better off charging a flat fee of $65 or else the amounts (5- X). (Note: It is not generally true that E()- The repair facility Select--- be better off charging a flat fee of s65 because E150 [(5 - x)] -

P(A)=0.55,P(B)=0.58,P(B∪A)=0.86 Find the following probabilities. P(A∩B) =  P(B|A) =  P(A|B) =