Problem 3. Jackpot Dilemma You are invited on a TV program where you have the opportunity to win a jackpot worth eight million dollars. You enter the stage and there are four boxes on the table. Only one of the four boxes has the jackpot money. Without other information, you can assume that the probability of each of box having the prize is uniform. 8!) Q (g The host rst asks that you make a choice among the four boxes. You simply choose a random box and remove it from the table. For the box that you choose, what is the probability of you hitting the jackpot? What is the sample space and what are the probabilities associated with the elements in the sample space? {3 g) 63 After a while, a magician comes to the stage and opens up one of the three boxes left on the table (not chosen by you). It turns out to be empty. The host then says: \"Here is your million dollar chance. You get to either keep the box you are holding or change your choice to one of the unopened boxes on the table.\" Now what is the probability of the box in your hands containing the prize? And what is the probability of one of the unopened boxes on the table containing the prize? What does the host mean when he says, quite literally, \"your million dollar chance\"? Should you change the box you've chosen? Explain your answer using conditional probability