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Lets assume that at an exam, students must pick their subject from a pile of envelopes. Some of the subjects are easy and some are hard. The students don't put the envelope back into the pile after picking. Do those who pick first have a better chance of picking a easy subject?

More lets assume that the students know how many subjects are easy and how many are hard.

This is fundamentally an "Urn problem" without replacement.

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No, if noone knows anything about the envelopes.

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  • $\begingroup$ Yes...so depending on the percentage of hard vs easy subjects maybe it's better to pick first(if the percentage of easy subjects is big) or to pick last (if the percentage of hard subjects is big). $\endgroup$ – user112056 Nov 28 '13 at 12:18
  • $\begingroup$ But noone knows which envelopes have been selected, right ? $\endgroup$ – Peter Nov 28 '13 at 12:20
  • $\begingroup$ Right. They all know just the percentage. $\endgroup$ – user112056 Nov 28 '13 at 12:24
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    $\begingroup$ Since the envelopes aren't being replaced, and none of the other students learn anything when one student opens an envelope, you can model this as all students draw an envelope and then open them simultaneously. So clearly then they all have the same chance of getting a hard or easy subject. $\endgroup$ – postmortes Nov 28 '13 at 12:27
  • $\begingroup$ Yes, that is a superb argument. $\endgroup$ – Peter Nov 28 '13 at 12:29

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