A batch of 50 different automatic typewriters contains exactly 10 defective machines. What is the probability of finding:
(a) At least one defective machine in a random group of 5 machines?
(b) At least two defective machines in a random group of 10 machines?
(c) The first defective machine to be the kth machine taken apart for inspection in a random sequence of machines?
(d) The last defective machine to be the kth machine taken apart?
I believe that finding at least two defective machines would be :
P(x≥2) = 1 − P(x<2) = 1 − P(x=0) − P(x=1)
and similarly for at least one defective machine (as in part (a)). I'm not sure whether this would be correct or not and I have no idea how to do parts (c) or (d) at all.