"Mensanator" <firstname.lastname@example.org> wrote > But I still say > "What is the probability that the i-th part you examine will be defective?" > means to calculate the probability before inspection begins.
Fine. Before the inspection begins it is clear that the probabilities for each inspection will change as the process goes along. Thus for i=1 the chance will be 1/100, for i=2 it will be 1/99 and in general it will be 1/(101-i).
> If playing Russian Roulette, we can ask > "What is the probability that the i-th player will shoot himself?"
As I understand it, people playing Russian Roulette spin the cylinder after each try -- the equivalent of throwing good parts back into the pile so that you've always inspecting a random one out of a hundred.
In inspecting parts, by contrast, the process has the purpose of identifying bad parts and separating them from good parts, so the odds necessarily change on the basis of knowledge -- and this process is understood beforehand.
This is, contrary to what somebody here said, a good homologue of the Monty Hall problem -- so the stupid teacher in this class can at least take some comfort from the fact that IQ champion Marilyn von Savant got that one very publicly wrong for endless tiresome months.