Problem 2 [20 points]. Consider the Monty Hall problem that we discussed in class. Instead of having three doors with one door having a price, now suppose there are four doors with two doors hiding goats behind them and one door having a price behind it. The other door has nothing behind it. To play the game, the guest will pick a door and the host will then reveal another door with a goat behind. The guest can then choose whether to stick to the original choice or switching. Should the guest switch? What is the probability of winning if the guest switches