Problem 1. There are three boxes (A, B, and C) and one of the boxes has a gift certificate for a brand new iphone XSMAX. Gheorghe, the winner of the lottery, is asked to pick which box holds the certificate. If he picks the right box, he will get to keep the prize, a new iphone XSMAX. Once Gheorghe picks a box, Partha, the host, opens an empty box and asks Gheo- rghe whether he wants to change his mind and pick the other box. Suppose Gheorghe picks box A. Partha shows box B empty and asks Gheorghe if he wants to change his mind and switchs to box C. Use Bayes' Theorem to analyze whether Gheorghe should switch to box C