Question

)A ship is fitted with three engines A, B and C. These three engines function independently of each other with probabilities ½ , ¼, ¼ respectively. For ship to be operational atleast two of its engines must function. Let E denote the event that the ship is operational and E1,E2 and E3 denote the events that engines A,B and C are functioning. Then validate the following.
(a). P(E1C / E) = 3/16
(b) P(E / E2) = 5/16
(c) P( Exactly two engines of the ship are functioning / E) = 7/8.