I thought the best way to tackle this was thinking of it as a binomial probability question. Then some rather obvious logic hit me in the face.
For those who remember their school maths, the total number of combinations the marbles can be drawn is 30 C 5 or 30!/(25!x5!) = 142506
Now of those 142506 combinations, how many of them have the last marble as black? The answer is quite simply 1 in 6.
Therefore there is theoretically no difference between being first or last.
I can't prove it, but I reckon if you ran the test a sufficiently large number of times, it would not matter when you drew your marble (1st, last, 7th, 18th etc), you would get black 1 in every 6 times.
Happy to hear a conflicting opinion if someone can point out a flaw in the logic
