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Simulating Discrete Random Variables: Roulette

I'm sure most of you teaching AP Statistics use a similar approach to introducing discrete random variables to the students.  We typically choose some sort of "game of chance" to find probabilities and put monetary amounts on winning/losing.  In the past I have done the "Pick 4" lottery ticket (see link below). But let's face it, our students can't actually play this many, many times for a simulation (which is what I like to model in class). Well I guess we could- but the chances of winning are so slim that I couldn't imagine one of the kiddos actually doing so.  Anyhoo... roulette it is!

 Before I get into my experience, here are some links to a few options for other intro to discrete random variables activities (I haven't actually used all of these, but there are some interesting ideas):

Now, my district does not purchase textbooks for students (or teachers), so we are able to use any resource we find.  I will say that many teachers are not liking this (even after about 6 years of the policy), but I find it very freeing!  I have the autonomy to choose what is best for my students and me.  Of course, for the higher-level math classes, it is nice to have one go-to reference;  mine is TPS4e, which means we follow the State/Plan/Do/Conclude protocol for simulations.  Here is what happened in this lesson:

State A roulette wheel has 38 numbered slots, 1-36, 0, and 00.  The odd numbered slots from 1-36 are red and the even numbered slots are black.  Both 0 and 00 are green slots.  You may only guess red or black for this simulation- if "the wheel" lands on green, it is an automatic loss.

Plan This is where you can have students do a Think/Pair/Share.  Their task is figure out how to use a random number generator to play roulette.  Almost all groups have a similar approach, but some can be a bit out there... and still correct!

Do Finally, they get to carry out playing roulette.  In pairs, each student will guess "red" or "black" and their partner will work the wheel (calculator) and keep track of win or loss- this will happen 20 times per student.

Conclude Because I like to have students moving during class, I have them put tally marks on the board for their outcomes.  We find the probability of winning and have a class discussion on what this means for the House if we were actually playing in a casino.


Now we put this in context of discrete random variables:





After the simulation, we find the theoretical probability of winning roulette and discuss how close our class was (it's typically pretty close) and find the expected value.  Of course, we bring it back to context and what this value means for a casino. 

Hopefully, this will help put discrete random variables in a new perspective and ease any anxiety teachers (especially new to AP Statistics) have!

Thanks for making it this far :)

~SSB



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