Using Coin Tosses to Teach Basic Probability

When teaching basic probability, I like for students to really "see" their work. I start by going over the Theoretical Probabilities for certain events: rolling two dice, tossing a coin and pulling a single card from a full deck. In this part of the lesson, we look at what "should" happen when we perform the experiment. A good example is tossing a coin 100 times. In theory, the coin should land on heads 50 times and on tails 50 times. How often does this happen in reality? Not very often -as a matter of fact, in using this project numerous times in the last ten years, it has never happened. But, we are only looking at what "should" happen.

Once I have gone over the theoretical probabilities, I then discuss the activity that we are going to do. I give each student a worksheet with the following instructions:

Pair up with a partner. One person is going to toss a coin; the other person will record the results. Record an "H" if the coin lands on heads and a "T' if it lands on tails. Do this for 100 tosses of the coin. When you have completed 100 coin tosses, swap roles and repeat the experiment.

Once both partners have completed the coin toss, I have them to make a frequency distribution of their data. Since they have 200 total coin tosses, the theoretical probability is that we should get 100 head and 100 tails. I have the students to record their data on the board. Each group lists their total number of "Heads" and "Tails." We then make a total for the entire class. We compare the data that we get (empirical probability) to our 50/50 Theoretical Probability. Normally, when we combine the data gathered by the class, we get closer to the 50/50 split that "should" happen.

After we look at the data for the whole class, I pull data for years past. I list the semester and the class data in a column on the board. I do this from the time I started using this lesson through the present class. We total the data over several years and again compare to the 50/50 split that we hope to get. The more data we add, the closer we get to 50/50. As of this semester (Spring, 2008), I am still not at a 50/50 split. I am close, but not perfect -at least in theory!