introduces the concept of probability and defines it. Wefrequently use probability in our daily lives to make decisionswhen we are not sure about the outcome. Read the followingmind-boggling famous problem and decide.
“The Monty Hall problem" is a famous probability related conundrumfaced by participants on the game show Let’s make a deal thatpremiered in 1963 and is still running some markets around theworld. At the end of each day’s show, a contestant was invited tostand with host Monty Hall facing three big doors: Door no. 1, Doorno.2, and Door no.3. Monty explained to the contestant that therewas a highly desirable prize behind one of the doors and a goatbehind the other two doors. The player chose the three doors andwould get a prize whatever was behind it. The initial probabilityof winning was straight forward. There were three two goats and onecar. As the participant stood facing the doors with Monty, he orshe had a 1 in 3 chance of choosing the door that would be openedto reveal the car. However, Let’s make a deal that had a twist,which is why the show was immortalized in the probabilityliterature. After the contestant chooses a door, Monty would openone of the two doors that the contestant had not picked, alwaysrevealing a goat. At that point, Monty would ask the contestant ifhe would like to change his pick-to switch from the closed doorthat 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 bestanding there on stage. Two doors would still be closed, nos. 1and 2. If the valuable prize was behind no. 1, the contestant wouldwin; if it was behind no. 2, he would lose. But then things gotmore interesting: Monty would turn to the player and ask whether hewould like to change his mind and switch doors (from no. 1 to no. 2in this case). Remember, both doors were still closed, and the onlynew information the contestant had received was that a goat showedup behind one of the doors that he didn’t pick.”
Address the following question in your post:
• Should the contestant switch the door? Make sure to discuss thereasons why he needs to switch or not switch.
