In a previous post, I talked about ways to use random number generators on a calculator to simulate rolling dice, or flipping a coin, using the fx-991EX scientific calculator. Probability is such a fun way to explore mathematics, especially when you can collect the data and really relate the concepts of sample size, theoretical probability, experimental probability and measures of center to a real-world application. When I was teaching in the middle and high schools, my students and I had so much fun doing math – i.e. tossing coins, rolling dice, picking cards, using candy to explore sampling, creating surveys and collecting data, etc. Unfortunately, especially in this strange new world of distance learning, doing probability experiments with real objects is a bit harder, since everyone is remote. Having technology and being able to do probability simulations virtually is a great advantage, so today I am going to revisit probability simulations, looking at Casio’s newest graphing calculator, the fx-9750GIII, which has an add-in app specifically for Probability Simulations.

The emulator software for the fx-9750GIII comes with the Probability Simulation menu already installed, which is fantastic, since as a teacher, you could have this on your screen while teaching virtually with students, and run the simulations and students collect and record the data. It would be ideal for students to have the hand-held version as well, in which case the Probability Simulator menu needs to be added to the hand-held menu via computer download. I have provided a how-to download the app video below, along with an overview of how to use the Probability Simulator.

The Probability Simulator is really powerful because it allows you to quickly collect lots of data, see the changes as data is collected both in a table and graphically. When working with students doing the data collection by hand, the fewer samples they collect, the less likely they are to ‘match’ the theoretical probability that is predicted for the outcome. So, tossing a coin, theoretically should yield 50/50 heads/tails. But, if students only toss the coin 10 times, they are more likely to not match the theoretical, and maybe heads seems to be more likely. The idea behind the Probability Simulator is that you can start with a small number of samples, and then build, and go up to 999 data samples of the experiment (which in a classroom situation would be unrealistic time-wise). What students can see as you increase the number of samples is that the theoretical probability becomes more likely, reinforcing the idea that sample size/number of trials has an impact. There are 6 different simulations that you can run with the Probability Simulator – coin toss, dice roll, spinner (spinning to land on 4 possible numbers), marble grab (five different types of marbles), a card draw, and then random numbers. You can set the number of trials. What I love is there is a visual of the ‘trial’ (dice rolling, spinner spinning, etc), as well as then a graphical display of the outcome and a table display. Students are provided with multiple representations of the situation which really helps them make connections. The last two options, card draw and random number, don’t show a graphical display. Instead, after collecting your data, you have the option to store the data to Statistical Lists. When you then go into the statistical menu, your lists are populated and you can then decide which lists and what types of graphical displays make sense for the data collected. You can actually do that with all the different simulations – store the data and go into the statistical menu and look at different plots, such as box-and-whisker, pie, scatter….whatever might make sense. But the first four auto-show a bar graph along with the table as the simulation is running, which is a great visual.

Here are two videos related to the Probability Simulator – the first one is how to download the add-on app to the hand-held fx-9750GIII calculator and the second one is an overview of the Probability Simulator app in action.

- If you have the fx-9750GIII hand-held graphing calculator and want to add in the Probability Simulator app to the menu (and also the Physium), here is the link to where those are located: https://edu.casio.com/download_service/en/download/index.html
- Here is the overview of how to add in the app (or additional apps as well): fx-9750GIII – Downloading and Adding Add-in Apps
- This video is an overview for the Probability Simulator app: fx-9750GIII Probability Simulator App Overview

Be sure to visit Casio Cares: https://www.casioeducation.com/remote-learning

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