The connection with the stopped watch is that in both cases there s a solution that works only if you ask the question for which it the watch or the simple solution produces the correct answer It s like using Pythagoras theorem to determine the length of the third side of a 6 8 X triangle without saying anything about whether the triangle is a right triangle Yes X is 10 if the triangle is a right triangle but Pythagoras theorem only applies if the triangle is a right triangle so unless it s given that the triangle is a right triangle or you can somehow show the triangle must be a right triangle based on what s given using Pythagoras theorem is unjustified Similarly showing that the unconditional probability of winning by switching is 2 3 for the MHP which is what the simple solutions do when asked about the conditional probability is not a complete answer unless you also say something about why these two probabilities must be the same You don t need to take my word for this it s exactly what Morgan et al and Gillman and Lucas Rosenhouse and Schepler and Rosenthal and Grinstead and Snell and the others I keep mentioning are saying And since Wikipedia doesn t care what you think or what I think and there are plenty of reliable sources that present unconditional solutions without justifying their answer must be the same as the conditional probability it s perfectly fine to present these sorts of solutions What I m saying is NOT fine is presenting these solutions as if they are the undisputed way the problem should be approached This isn t a difficult concept I m perplexed why we have to keep arguing about it