Recently I attended a workshop on probability, I was asked the following question but I did not find a way to solve it. A discussion on this question can help to learn something new.
We were told that, We are guests in a game show and close to win a great fortune. The quiz master asks us to choose one of three (closed) doors. She explains that behind one of them awaits you a million Euros. Once you fixed your choice the quiz mastress opens one of the other doors and shows you that this was only a goat. She gives you a final chance: you may either retain your door or switch to the remaining closed one.
(i) Say door 3 is opened. How can we Calculate the conditional probability that our door is the winning one given that the door 3 is a fail, and its complement.
(ii) How to Calculate the unconditional probability that our door is the winning one, and its complement.
Thank you in advance.