1.Solve Monty's Hall problem using Bayes Theorem and conditional probabilities.

2.Suppose that Monty's Hall problem is modified like the following: after you chose a door, the

host asks you to pick one of the other two doors which will then be eliminated from the choice

of three. (No door will be opened by the host.) Having done that, you are then allowed to either

stick with your original door or swap to the remaining door. Do you still want to switch?