a. play the game 100 times using https://montyhall.io/. You get to decide which strategy to use and when. For example, you may use only one strategy, you may randomly mix it or you can do one strategy 50 times and then try the other strategy 50 times. When complete take a screen shot b. Use a probability tree to find the exact probabilities for the switch strategy. Start by having you pick with equal probability the car, goatl or goat2. If you had picked the car in the first round, then with 100% probability, you will get a goat the second round. Since Monty will reveal where the other goat is, if you had picked a goat, then with 100% probability, you will get the car the second round. c. For the stay strategy, there is really only one round, as you don't use the information Monty provides. You have a one third chance of getting the car and that's how it ends. 2.Suppose that a small chest contains three drawers. The first drawer contains two $1 bills, and the second drawer contains one S1 bill and one $100 bill. These bills are enclosed in identical envelopes. Suppose that first a drawer is selected at random and then one of the two bills inside that drawer is selected at random. We can define these events; A = the first drawer is selected, B =the second drawer is selected, C =a $1 bill is selected a. Suppose when you randomly select one drawer and then one bill from that drawer, the hill you obtain is a S1 bill. What is P(B | C), the probability that the second bill in this drawer is a $100 bill? Answer this guestion intuitively without making any calculations. b. Use the relative frequency concept of probability to estimate P(B | C) as follows. First select a drawer by flipping a coin once. If head, the first drawer is selected and you know that both A and C has occurred. If tail, the second drawer is selected: flip the coin a second time and if you get a head, this will indicate that you have selected the envelope with $1, in other words B and C has occurred. If you get a tail for the second flip, then C has not occurred. Repeat this process 50 times. How many times in these 50 repetitions did the event C occur? What proportion of the time did B occur when C occurred? Use this proportion to estimate P(B | C). Does this estimate support your guess of P(B | C) in part a? c. Calculate P(B | C) using the procedures developed in this chapter (a tree diagram may be helpful). Was your estimate in part b close to this value? Explain. My Game Stats WHEN I'VE SWITCHED: - Win Rate: 68% - Wins: 34 - Losses: 16 WHEN I'VE STAYED: - Win Rate: 32% - Wins: 16 - Losses: 34