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A ship is fitted with three engine es E1...

A ship is fitted with three engine es `E_1,E_2a n dE_3dot` the engines function independently of each other with respective probabilities 1/2, 1/4, and 1/4. For the ship to be operational at least two of its engines must function. Let `X` denote the event that the ship is operational and let `X_1, X_2a n dX_3` denote, respectively, the events that the engines `E_1, E_2a n dE_3` are function. Which of the following is/are true? a. `P(X1C"|"x)=3/(16)` b.`P` (exactly two engines of the ship are functioning `|X` ) `=7/8` c. `P(X"|"X_2)=5/6` d. `P(X"|"X_1)=7/(16)`

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