Curiousity [glad I'm not a cat]

Ishuda

Elite Member
Joined
Jul 30, 2014
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3,345
Don't know whether it's because I'm lazy or just can't figure it out [probably both :)]: Take n things and put them in a container. Now draw them out 1 at a time without replacement [with 1/(m-k+1) probability of choosing a particular thing on the kth draw] and discard (use) it. When you get down to m things, refill the container to n things again [before drawing the (m+1)st] and start the process over again. Repeat this x times. What is the probability, P(x), that at least 1 one of the original things remains in the container.

If x is 1 [we have refilled the container 1 time and haven't started the drawing process for round 2], then obviously we have P(1)= 100%. since there are m of the originals left in the container but what about P(2), P(3), ,,,?

If you are interested: What got this started is we have several bottles of acetaminophen and I got to thinking about what if we refilled them from a single bottle when they get low rather than just replace a complete bottle. What would be the probability that I would use an 'expired pill'? [not that I was worried about it, I was just curious] Actually the answer depends on how often I take one (or two) of the pills but, ignoring that, I think the problem boils down to the above.
 
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