What concept is Mr. Miller teaching by having students explore combinations of coin flips and die rolls?

Mr. Miller is teaching the concept of sample space by having students explore combinations of coin flips and die rolls. The sample space refers to the set of all possible outcomes of a given experiment. When students flip a coin, there are two possible outcomes: heads or tails. When rolling a die, there are six possible outcomes: 1 through 6. By combining these two activities, students can create a sample space that lists all the possible outcomes of a coin flip combined with a die roll.

For example, if a student flips a coin and rolls a die, the sample space would include pairs such as (Heads, 1), (Heads, 2), ..., (Tails, 6). This hands-on exploration helps students understand how to systematically enumerate outcomes and highlights the concept of a sample space in probability theory, laying the groundwork for more complex ideas in probability later on.