Guys, the meaning of the question is quite obvious.
What is the new sample information? That we have found a defect.
So, if we have randomly sampled and found a defect, what is the probability that another random sample taken will be a defect?
What changes when we sample and find a defect? P(W) and P(W'), where P(W)= probability of machines working properly.
So, obviously we need to find P(W|D) (or P(W'|D) as they sum to one) and then reapply the method of a) (that is, reapply P(W)*P(D) + P(W')*P(d) with P(W|D) and P(W'|D), where P(d) is the probability of a defect when not working properly)
P(W|D) can either be found using Bayes therom or a contigency table, and is approx 0.716 from memory, making P(W'|D) approx .284. When you put that into the aforementioned probability equation [as P(D) and P(d) remain constant] you get the new probability of defect as .0568 approx.