MHP  The player is informed about the rules but still in the dressing room before being on stage she is asked whether she will switch Simple solution no need of conditional probs   The player is informed about the rules and after she made her first choice the host tells her he will shortly open one of the remaining doors Before doing so he asks her whether she likes to switch to the door he will leave closed Simple solution possible although one formally has to condition on the players choice   The player is informed about the rules and after she made her first choice the host opens one of the remaining doors He then asks her whether she likes to switch The solution needs to consider the conditional probability  For me only the rd form is of interest