The Monty Hall problem is named for its similarity to the Let'sMake a Deal television game show hosted by Monty Hall. The problemis stated as follows. Assume that a room is equipped with threedoors. Behind two are goats, and behind the third is a car. You areasked to pick a door, and will win whatever is behind it. Let's sayyou pick door 1. Before the door is opened, however, someone whoknows wh at's behind the doors (Monty Hall) opens one of the othertwo doors, revealing a goat, and asks you if you wish to changeyour selection to the third door (i.e., the door which neither youpicked nor he opened). The Monty Hall problem is deciding whetheryou change your selection or not that has a better chance ofwinning the car . It’s common sense that if not to change, theprobability of winning is 1/3 but what about changing theselection.

Simulating this game using SAS, for each round, program the following, 1) Assigning two goats and a car to three doors randomly 2)Picking a door randomly 3) Picking one of the two remaining doorsto open but must showing the goat 4) Changing the selection to theremaining door 5) Deciding the result Repeating these steps for 100round s , generating a data set including the following fivevariables, the round number, the door the car is in, the doorchosen initially, the door chosen after switching, and theresult(win/lose). Showing the data set and r eporting the frequency of the i nitial door chosen, the frequenc y of the door chosen atthe end, the average rate of winning.