I have a bag of 60 marbles(N=60). I can only examine 30 random marbles (n=30) at a time. After each trial, I replace the sampled marbles back in the bag. How many trials will it take for me to examine each marble at least one time?
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$\begingroup$ Change "424" to "60" and "5" to "30" to convert the duplicate into this question. $\endgroup$– whuber ♦Commented Jul 6, 2017 at 15:04
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Unless I'm missing something here, there is no finite number of trials that will guarantee you see each marble at least once.
Since you replace the marbles after each sample, then hypothetically speaking if you took $x$ number of samples, you could sample the same exact marbles all $x$ times with positive probability.
If you were to take an infinite number of samples however, the probability of never getting any one marble would go to zero, and so you'd get every marble at least once with probability one.
