Simulation vs Probability
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.
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.
Probability
Probability
Probability is a number from 0 to 1 measuring how likely an event is, with 0 meaning impossible and 1 meaning certain.
Probability measures the long-run relative frequency of an event over many repetitions. For equally likely outcomes, . For example, rolling an even number on a fair six-sided die has probability . Over many rolls the fraction of even results settles near this value, an idea called the law of large numbers.