Each hypothesis leads to an expected value of (X-1)/(m-1)
(X-1)/m, because the emptied envelope is shuffled back into the set.
Oh, whoops, I didn’t read the question correctly. Drat, then it’s not Laplace’s rule of succession.
In fact, that messes up pretty much everything—I’ve finally found a use for the retract button.
Well, not everything—it isn’t Laplace’s rule of succession, but if you correct the mistake, you’ve pretty much solved part 2. Instead of a fixed value you get an equation you can solve for m.
That’s true. It also invalidates my answer for part 1, which is a bit trickier to correct, because you no longer have the nice symmetry.
(X-1)/m, because the emptied envelope is shuffled back into the set.
Oh, whoops, I didn’t read the question correctly. Drat, then it’s not Laplace’s rule of succession.
In fact, that messes up pretty much everything—I’ve finally found a use for the retract button.
Well, not everything—it isn’t Laplace’s rule of succession, but if you correct the mistake, you’ve pretty much solved part 2. Instead of a fixed value you get an equation you can solve for m.
That’s true. It also invalidates my answer for part 1, which is a bit trickier to correct, because you no longer have the nice symmetry.