Students will describe how the distribution of a random sample of outcomes provides information about the actual distribution of outcomes in a discrete sample space.

• Students will compare the distribution of a discrete sample space to distributions of randomly selected outcomes from that sample space.
• Students will identify the structure that emerges as more and more data are added to the distribution (that is, the features of the distribution of random processes stabilize as the sample gets larger).
• Students will recognize that relative frequencies of particular outcomes after few observations are more likely to deviate substantially from expected values than are relative frequencies based on more observations.

• distribution
• variability
• sample space
• outcome
• relative frequency

This lesson involves generating single outcomes from a given sample space and observing how the distribution shape develops as the number of observations increases.
As a result, students will:

• Compare with their classmates' distributions to note the large variability that can occur in relative frequency measures with only a few observations.
• Observe the generation of a very large number of outcomes to visualize the law of large numbers.
• Observe how the probability of a specific outcome stabilizes as the number of observations increases.