Q. A ship is fitted with three engines and 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 denotes the event that the ship is operational and let and denote, respectively the events that the engines and are functioning.
Which of the following is/are true?

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[exactly two engines of the ship are functioning]

Solution:

PLAN It is based on law of to ta l probability and Bay 's Law Description of Situation It is given that ship would work if atleast two of engines must work. If X be event that the ship works. Then, either any two of works or all three engines works
Given ,
.

Now ,

(d)

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