Monty Hall Problem
This may be a longer lesson than most. May need one and a half sessions.
The Monty Hall Problem
Teacher to watch this to get some understanding:
https://mikesmathpage.wordpress.com/2017/10/01/exploring-the-monty-hall-problem-with-kids/
Do not show this to the students.
Explain that this is a famous Mathematical question that even adults sometimes get wrong. And we are going to use testing to prove one outcome over another.
The problem is as follows:
You have arrived at the final round of a game show. The host shows you three doors (draw three doors on the board and label them Door 1, Door 2 and Door 3), and tells you that behind one of the doors is a new car. The other two doors have nothing behind them. If you open the door with the car behind it, you win the car. If you open a door with nothing behind it, you win nothing.
The host asks you which door you would like to open. (Ask the students what the chance of us opening the correct door is. They should say 1/3.)
The host then opens one of the doors that has nothing behind it, and asks you if you would like to change from the door you chose, to the other door that is not open.
Should you swap or not? Does it matter if you do or not?
Explain that we are going to conduct a controlled experiment to work it out.
The students will be conducting an experiment to answer these questions. You will need to demonstrate how to use the supplied learning materials.
You will need to demonstrate with them first:
Students will need to work in pairs. Show how to fill in the first sheet, where the question is asked each time. One partner chooses where the car is hidden, and moves a counter onto door one, two or three. The other partner then rolls the dice, which decides what door they pick, at random. The sheet is filled in as they go. There is no opportunity to switch doors in this version. Record down how many wins out of 18 tries.
The second sheet is to record the same experiment, but this time one losing door is ‘opened’ revealing that there is nothing behind it, and the contestant MUST change to the remaining door. Again, the sheet is filled out to record the frequency of wins.
Each pair should have one die and this sheet:
Monty hall problem.docx PRINT 2 PER PAGE FOR PARTNERS
At the end of the lesson, discuss findings. (It should show that you win on average 1/3 of the time if you do not change, and 2/3 of the time if you do.