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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//X)=3//8`

B

`P(X//X_2)=7//8`

C

P (Exactly two engines are functioning )=7/8

D

`P(X//X_1)=7//16`

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The correct Answer is:
D
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