POW 11: Let’s Make A Deal
1. Problem Statement: For this Problem of the Week we were required to find out if our chances of winning Let’s Make A Deal were higher if we switched to the other door or stayed with our original door after a worthless prize was revealed behind one of the doors we did not chose. The game show host knew what was behind each door, so every time he would reveal something worthless behind one of the doors you did not choose after you made your first choice. Then he would allow you to switch doors from your original door to the other remaining door. Basically, we evaluated if switching or staying worked best.
2. Process: At first when I saw this problem, I thought it was a joke because the answer seemed obvious. But, after closer examination I realized I was harder than I had originally thought. So to help us with problem Andrew and I completed the assignment Simulate a Deal. Ms. Favazza posted a website on the Moodle that replicated the game show and exactly how it worked so we used that to simulate what could happen when we used the two strategies to win the car, switch doors or stay with our originally door. Right off, we realized switching was winning us the car a lot more than staying. Out of the 20 times we played while staying with our original door we won the car 5 times. And when we switched, we won the car 14 out of 20 times. Soon after I completed the assignment I realized that switching would definitely win you the car more because when you make your first choice on what door you want, there is a 2/3 chance you picked a goat, but when you switch, those odds are now in your favor for winning the car.
3. Solution: When you switch doors, you have a 2/3 chance of winning the car. When you stay with your original door, you have a 1/3 chance of winning the car. I first found the probability of your chance of winning the car when you stay with your original choice by simple logic. There are three doors to choose from at the...
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