Question :

An Engineering system consisting of n components is said to be k-out-of-n system $\displaystyle (k \le n)$ if and only if atleast k of the n components function. Suppose that all components function independently of each other with the probability $\displaystyle \frac{1}{2}$. Find the conditional probability that component 1 is working given that the system funstions, when k=2 and n=3.