Monty Hall Problem

In my Foundations 30 class we started our probability outcome last week.  As a "hook" to the outcome, we spent a day exploring the Monty Hall Problem.  For those of you who grew up watching Let's Make A Deal, you will know who Monty Hall is!  For those of you who don't, simply google Monty Hall Problem.  It is a mathematical paradox that has had many people talking about it.  Most of my students did not know about this show or who Monty Hall is.  I explained to them a bit about the show and we watched a short clip on youtube about the show so they had some background.  I then explained to them the finale of each show - three doors presented to a contestant, 2 of which had goats and one which had a prize - typically a car.  The contestant had to pick one door, Monty Hall then opened one of the other doors where he knew there was a goat, and then asked the contestant if they wanted to stay with their original choice or switch to the other door.  I left it at that and gave the students a few minutes to discuss whether they would stick or switch and why.   As I walked around and listened to the conversations I was impressed at what they were thinking.  Some were saying they would stay because that was their gut feeling and they would regret if it was in their original pick, others said they would stay because you had a 50-50 chance anyways, and a few said they would switch because they would increase their chances.  It was also interesting because the level of engagement was higher than normal and I had a couple of students googling the problem on their phones!   After a few minutes I had some students share their thoughts.  It was interesting as how most felt it was a 50-50 chance and the few who thought the chances would increase were shy to share why since they weren't the majority!   I didn't give anything away, just listened and asked why they felt the way they did.   I then shared how we had done this as a group of teachers last year and that we were also split on our opinions.  We then watched a mythbusters youtube video on this problem.  It explained and showed that a person actually doubles their chances of winning if they switch.  That surprised many of the students.  This was a good hook for probability.

The next day was when I realized how engaged some students were and how great of a hook it was.  I had a student who struggles with math, doesn't have regular attendance and often comes late say to me "you know I hate math but that problem we did yesterday...I couldn't stop thinking about it and I hated that... but I still think I'm right with 50-50 and it bugged me and was all I thought about."  AWESOME!!!!!  When you can get a student who openly hates math to THINK about a math problem, you know you have engaged them!   I only wish I had a bag of magic tricks to do this every day!  Maybe by the time I retire I will have this bag of tricks!  For now I'll take it when I can and be satisfied that I was able to succeed even once for now!  And not that I'll stop looking, as I'm always looking, but I am happy for the feedback that I received!