Probability Simulation with the fx-991CW Scientific Calculator
- Karen Greenhaus
- 4 days ago
- 3 min read
When I was teaching middle school, I always loved the probability section because we would do some engaging activities with dice, cards, coins, candy, etc. It was a fun way to compare theoretical probability to experimental probability and get students collecting data and doing mathematics.
An obvious experiment that many start with is tossing a coin and determining the probability that it will be heads or the probability it will be tails. The theoretical probability is that there are two outcomes, 1 heads, 1 tails, so probability for both is 1/2. However, if you have students actually experiment and record how many heads/tails out of a specific number of tosses, it is more often not 1/2 (50%), unless you do a large number of flips (i.e. collect a larger sample). I used to have pairs of students flip a coin 10 times, then we would compare and see how many came up with the theoretical probability. There were usually a couple, but more that did not. We would do another 10 tosses but combine group data and compare, and finally combine all the data from the class (so a much larger sample) and compare. The idea being that the more samples, the closer you get to the theoretical probability.
Similar things can be done with cards - i.e. what is the probability of drawing a face card? Or a specific number card? Tossing dice is another great one - you can do one die and the probability of getting a specific number, or a really fun one is rolling two dice and summing their face value and determining the probability of getting a 7. Students have to first think about all the different combinations of sums, how many of each, etc. The possible combinations of sums is 36 (note, (2,1) and (1,2) would be counted as two separate ways to get a sum of 3). The number of different ways (works best if you use two different colored dice) to get a 7 is 6, so theoretical probability is 6/36=1/6. It's then a nice connection to the why craps uses the 7 as the 'crap out' roll - it is theoretically more likely for someone to roll a 7 and lose for the whole table than any other sum.
There are obviously many things you can do with basic probability. I had a bucket of pennies, a bucket of different colored dice, many decks of cards, and would bring in candy (Skittles and M&Ms work great). You can use lots of hands-on things to make probability experiments fun and engaging. But....what if you don't have the means for these manipulatives? This is where you can use technology to 'simulate' things such as rolling dice or flipping coins, even picking a card from a deck.
Today's shared lesson is a brief one on probability using the Casio fx-991CW scientific calculator. Using the MATH Box menu, you can do dice and coin simulations pretty quickly, since those are built-in simulations. But, you can really expand that by using the table menu and the RandInt# function or Random Number function, to simulate tossing coins, rolling dice, and decks of cards, etc. The activity I’ve provided below specifically focuses on coins and random number probability using the table menu, but the video link shows you how to use the Math Box menu and Table menu to do coins, dice, and cards as examples.