7b. Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process.

If students are sick of theoretical probabilities and want a taste of more real-world stuff, here's where you'll knock their socks off. Rather than develop a probability model by assigning equal probabilities to each outcome, we're expecting students to use real-world data and generate probabilities that way. Fun.

Whether you give students the data or have them collect it themselves, they've got to look at the data and calculate probabilities the good old-fashioned way: dividing favorable outcomes by the total number of outcomes.

A good example of this is the spinning penny experiment. Each student could spin a penny on a flat surface a set number of times and count how many heads and tails they observed. The class could compile the data, and then, based on relative frequencies, the class can come up with an estimate for the probability that a spinning penny lands on heads and that a spinning penny lands on tails.

What's interesting about this example is that as a result of the distribution of weight in the penny (at least, this is true for the old pennies with the Lincoln Memorial on the back), tails will have a probability of about 0.8. The students should use the probabilities they discovered to answer questions such as, "If twenty pennies were spun, estimate how many heads will come up?"