A standard six-sided die is to be rolled repeatedly until a side appears a number of times equal to its number. In other words until the n-th n appears.
Let P(n)=the probability the game terminates with the n-th n.
Find the distribution of n.
Feel free to generalize for m sides.
Warning: I have not managed this past m=4.
(In reply to Solution for n=2 and 3, and some observations
57/81 + 17/81 + 6/81 = 80/81, not 1
The 17/81 should be 18/81. Something's missing from the set of terms you've added; there must be another term or one of the terms is wrong.
Posted by Charlie
on 2015-07-30 09:11:20