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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)/(16)`

D

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

Text Solution

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The correct Answer is:
B, D
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