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A ship is fitted with three engines E1, ...

A ship is fitted with three engines `E_1`, `E_2`, and `E_3`,. The engines function independently of each other with respective probabilities `1/2`. `1/4`and `1/4` ,and 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_2`, and `X_3` denote respectively the events that the engines `E_1`, `E_2` and `E_3`,are functioning. Which of the following is (are) true?

A

`P[X_(1)^(c)|x]=3/16`

B

`P[" Exactly two engines of the ship are functioning" "X]=7/8`

C

`P[X|X_(2)]=5/18`

D

`P[X|X_(1)]=7/18`

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