# SOCR EduMaterials Activities MontyHall

## This is an activity to find the probability of winning the Let's Make a Deal (Monty Hall) experiment.

Open http://www.socr.ucla.edu/htmls/SOCR_Experiments.html and use the scroll bar to find the Monty Hall Experiment. Once you find it, click on the About button and read about the experiment. There are two different versions of the game (standard or blind), but for this lab you will be using only the * standard * version of the game, which is the default setting of the applet. Answer the following questions:

**a.** There are three random variables (\( G, S, W \)) and one parameter (\( p \)) involved in this experiment. Describe what each one represents and what possible values they can take (you find it helpful if you run the experiment a few times before you answer the question).

**b.** Run the experiment just once (make sure \( p=1 \), which means the player always switches), make a snapshot of the outcome, and describe what happened (i.e. What door did the player chose at first? Which door did the host opened? Did the player switch? Did the player win?).

**c.** Perform 10 runs, take a snapshot.

**d.** Reset and perform 100 runs, take a snapshot.

**e.** Reset and perform 1000 runs, take a snapshot.

**f.** Using the three snapshots just taken, compare the theoretical probability distribution of \( W \) with the empirical distribution.

**g.** For the three snapshots taken, look at the graph on the bottom right hand corner, and compare the blue lines with the shaded red area. Where does the graph come from and how do they relate to the part (f)?

**h.** Reset and change \( p=0 \), which means the player never switches. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of \( W \).

**i.** Reset and change \(p=0.5 \), which means the player never switches half of the time. Perform 100 runs and take a snapshot. Describe the theoretical and empirical distribution of \( W \).