neq1's first paragraph refers to Jordan's scenario. neq1's second paragraph alters the scenario to be more like the one in the OP. In the altered version, we view the situation "from the outside". We have no way to specify any particular individual as I before the experiment begins, so our reasoning can only capture the fact that someone ended up in a room. Since we already knew that that would happen, we are still left with the prior probability of .5 that the coin came up heads.