Let’s make a deal is a game show in which contestants are given the opportunity to win a new car if they correctly choose the winning door three times in a row. In the first round, they must choose between 3 doors, one of which is labeled "win." In the second round and third rounds, they will choose from 2 doors, with one labeled "win." Before I watched the video, it is my belief that the probability of the chance of winning the new car is quite small. Initially the contestant chooses the first door which as we know from anyone who has ever watched is typically a dud or a “zonk” as I have seen it called. The contestant is then presented with the choice and opportunity to switch doors. This is the part where contestants are usually stuck with the face of question as to whether they should stick with the door they have chosen or take the leap of faith and choose door number 3. As we analyze the Monty Hall problem deeper using probability strategies and statistics it
is in the contestant’s best interest to choose door number three. It is best to compute the sample space of all outcomes. After the contestant has chosen door 1 there is a 1
3
chance that they will acquire the prize of a new car. However, after the second door is opened and revealed with only door 3 remaining the contestant has a 2
3
chance of acquiring the prize of a new vehicle. Often times on the show people are randomly choosing without considering the potential mathematical advantage of their choices. Although it is still not a guarantee to win the prize the probability of winning increases from 1
3
to 2
3
when the contestant chooses door 3 which I will analyze in depth later.
