Scenario: suppose you are going trick-or-treating on halloween. you are about to head home, but will stop at one last house before you leave. there are three houses for you to choose from (house 1, house 2, and house 3) and luckily your friend has already gone to each of them. according to your friend, two of the houses gave him apples and the other one gave him a king-size chocolate bar. your goal is to go to the "chocolate house" while avoiding the "apple houses." your friend is unwilling to give any other information at first, so you will decide which one to go to com- pletely randomly i. e. chance of picking house 1, chance of picking house 2, chance of picking house 3). suppose that you randomly choose house 1. before you head to the door, your friend stops you and tells you that house 2 is an "apple house."* now you are left with the decision to either stay with your initial choice of house 1 or switch and go to house 3. *for this game, no matter what house you initially choose, your friend will always reveal one of the others as an "apple house." if you initially choose the "chocolate house," your friend will randomly choose one of the other two houses to reveal. answer the following: 1. what would you do based on your intuition? stay with house 1, switch to house 3, or maybe flip a coin to decide whether to go to house 1 or 3? (this question is not looking for a correct answer. just what do you think intuitively). 2. define the events, a: "initially pick the chocolate house" and b: "end up going to the chocolate house." based on the scenario, determine p(a) and p(a). this is also given away in the example below.