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A ship is fitted with three engines E(1)...

A ship is fitted with three engines `E_(1),E_(2),and E_(3)` the engines function independently of each othe with respectively probability `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_(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)/(16)`

D

`P[X|X_(1)]=(7)/(16)`

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The correct Answer is:
B, D
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