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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 other with respective probabilities `1/2,1/4 and 1/6` .
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)e/(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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