Let A1, i=1,2,3,4,5 denote the probability that component ai is functional. Now, suppose that the events Ai have the fooling properties: I The status of component a4 and as are independent of the status of component a, a2, and a3. 0 A1 and A2 are independent. . P(A1)= P(A2)=0.5 . P(A3|(A1 n A2)) = 0.4 . P(A3|(Hj u Q) = 1/3 0 A1 Pl A2 and m form a partition. 0 A4 and A5 form a partition. Let C be the event that the system works. a) (5%) Find P( A3) b) (8%) Write an expression for C in terms of unions and intersections of the ms (and their complement) and find P(C) c) (7%) Given that the C occurs nd the probability that a3 is functional