If your 2 of 3 system is working, we must be in one of the following cases:
BGG
GBG
GGB
GGG
where G=good (working machine), and B=bad. Isn't the probability that any particular machine is working then 3 of 4?
Question :
An Engineering system consisting of n components is said to be k-out-of-n system if and only if atleast k of the n components function. Suppose that all components function independently of each other with the probability . Find the conditional probability that component 1 is working given that the system funstions, when k=2 and n=3.
Do you mean
In other words, the system has three components and the given condition is that the system functions when k = 2 and n = 3? This is very different to what you posted.
(Punctuation in the wrong place can completely change the meaning of something ....)