This idea is important. It's real-world stuff. You just MIGHT be on one of those daily game shows and be about to win a car if you could JUST choose the right door.....
Ok, so you're on the game show and have been really really successful guessing the right prices or spinning the dial wisely or guessing the word correctly or singing a song beautifully or something. Then the moment comes: you are offered the opportunity to win a brand-new car! A Porche, if you will. You are shown three doors: A, B, and C. Behind only one of these doors is the car; behind each of the others is a goat. Which one do you choose (presuming you would rather have the car than the goat)?
You've chosen door A out of A, B, and C. Then Monte shows you that there's a goat behind door B. He offers you the opportunity to switch to door C or stay with door A. Do you switch? Do you stay committed to door A?
There's a variety of ways to analyze this choice and at least as many blogs/videos/sites/pieces about it. Even Marilyn VosSavant weighed in on the topic in years past. She's a little hard to follow. Here's Sal Khan.
Watch this video.
This is a great video on winning a CAR or a GOAT.
Here's a website with a friendly tree diagram that does a great job showing you, using methods we used in class, whether you should switch or not.
My explanation includes 3 cases, each equally likely. Consider case one, you unwittingly choose goat (1). Case two, you chose goat (2), and in case three, you chose the car. When you chose, you don't know which of these three cases applies to you. When Monte Hall eliminates an option that he KNOWS is a goat, you would be making a winning choice in switching for the first two cases (ie, you'd be getting the car, ultimately), but in only one of the three cases would you be switching to get a goat. In other words, in only one of the three cases would you have initially chosen the car and switching would, in this singular case, be a bad idea. Therefore, 2/3 of the time, your switch would yield you the car instead of a goat. So YES, switch!
Here is a link to some other interesting probability problems. Look for the bus route problem and the birthday problem -- these are a couple of my favorites and standard fare for college statistics/probability classes. Choose one, do your best to understand what's going on, then write your post about this. Go ahead, google all you'd like.
