Indeed, indexing changing probabilities is very unintuitive for most people. Here's another fun one. There's two coins on the table that you don't see. The onl

Indeed, indexing changing probabilities is very unintuitive for most people. Here's another fun one. There's two coins on the table that you don't see. The only information provided is that a) one of them is tails b) the left one is tails What is the probability of both being tails? It's 1/3 in (a) and 1/2 in (b). The reasoning being: 1. At first both HH, HT, TH and TT are all equaly likely. 2. In case (a) we discard HH as an option, but in case (b) we discard *both* HH and HT.