A ship is fitted with three engines E 1 , E 2 and E 3 . The engines function independently of each other with respective probabilities 
, 
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 denotes respectively the events that the engines E 1 E 2 and E 3 are functioning. Which of the following is (are) true ?
Text Solution
Verified by ExpertsCHECK THE SOLUTION.
(b,d)
P(x 1 ) = 
; P(x 2 ) = 
; P(x 3 ) = 
P(x) = P(E 1 E 2 E 3 ) + P( 
E 2 E 3 ) + P(E 1 
E 3 ) + P(E 1 E 2 
) = 
P(x) = 
⇒ 
= 
= 
= 
P(exactly two / x) = 
= 
= 
P(x / x 2 ) = 
= 
= 
P(x / x 1 ) = 
= 
= 
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