[af3d]

The probability of guessing all eight correctly is 0.5^8 (or roughly 0.39%). The chances of such a thing happening by mere fluke are quite slim. Now personally, I would have preferred a few more glasses to be even more certain, but hey, for all practical purposes those results do seem fairly credible.

[yavgcnk]

Minor, but no it's 1/(8 choose 4) = 1/70 because there are 4 tea-first, 4 milk-first, and the lady tasting tea knows this.

Once the locations of the four tea-first cups are decided, the locations of the remaining milk-first cups are completely determined. (And there are 8 slots for those first 4 cups, hence 8 choose 4).

[af3d]

Ah yes, I stand corrected! In that case I suppose more trials really would have made the results more convincing, too....

[memco]

I wonder whether pouring them together in addition to the first or second cases would be useful for helping to ascertain how keen the sense was.