Unit 5 introduces the concept of probability and defines it. We frequently use probability in our daily lives to make decisions when we are not sure about the outcome. Read the following mind-boggling famous problem and decide.
“The Monty Hall problem” is a famous probability related conundrum faced by participants on the game show Let’s make a deal that premiered in 1963 and is still running some markets around the world. At the end of each day’s show, a contestant was invited to stand with host Monty Hall facing three big doors: Door no. 1, Door no.2, and Door no.3. Monty explained to the contestant that there was a highly desirable prize behind one of the doors and a goat behind the other two doors. The player chose the three doors and would get a prize whatever was behind it. The initial probability of winning was straight forward. There were three two goats and one car. As the participant stood facing the doors with Monty, he or she had a 1 in 3 chance of choosing the door that would be opened to reveal the car. However, Let’s make a deal that had a twist, which is why the show was immortalized in the probability literature. After the contestant chooses a door, Monty would open one of the two doors that the contestant had not picked, always revealing a goat. At that point, Monty would ask the contestant if he would like to change his pick-to switch from the closed door that he had picked originally to the other remaining closed door. For the sake of example, assume that the player has chosen Door no. 1. Monty would then open-Door no. 3; the live goat would be standing there on stage. Two doors would still be closed, nos. 1 and 2. If the valuable prize was behind no. 1, the contestant would win; if it was behind no. 2, he would lose. But then things got more interesting: Monty would turn to the player and ask whether he would like to change his mind and switch doors (from no. 1 to no. 2 in this case). Remember, both doors were still closed, and the only new information the contestant had received was that a goat showed up behind one of the doors that he didn’t pick.”
For this discussion:
Address the following question in your post:
• Should the contestant switch the door? Make sure to discuss the reasons why he needs to switch or not switch.