Random Digit Table vs Simulation
Both terms below come up in the same part of the course, and students mix them up. Here is each one defined on its own, side by side, so you can see where they part company.
Random digit table
Collecting data and study design
A random digit table is a long string of the digits 0 through 9 in random order, used to select a sample or assign treatments by hand.
To use one, give every individual a numeric label of the same length, pick a starting line, then read digits in groups of that length. Skip any group that falls outside your range of labels, skip any label you have already taken, and stop once you have the count you need. For example, to pick 3 of 40 students, label them 01 to 40 and read two digits at a time: 07, 63, 24, 07, 31 gives students 07, 24, and 31, because 63 is out of range and the second 07 repeats. The AP course describes random mechanisms such as a random number generator or drawing numbered slips of paper, and a table is the paper version of the same idea.
Simulation
Probability
A simulation imitates a chance process using repeated random outcomes, then estimates a probability from the fraction of trials that give the event.
A simulation lets you approximate a probability that would be hard to compute directly by running the random process many times. For example, to estimate the chance of at least one head in three coin flips, you can generate many sets of three random 0s and 1s and record how often a set contains a 1. The estimate is the number of successful trials divided by the total number of trials, (p-hat, the estimated probability). Running more trials generally gives an estimate closer to the true probability.