TABLE OF CONTENTS A random experiment is an experiment that produces random outcomes. For example, throwing a die is a random experiment in which each trial produces a random outcome from six possible outcomes, i.e., faces with one through six spots. The word "experiment" implies that the random situation under consideration is controlled. However, the word may also be used in a broad sense to mean any random situation that produces random outcomes, let us say, a nature's experiment.
A trial is a single instantiation of a random experiment. If a die is thrown ten times, there would be ten trials. The key concept to note here is that each trial produces exactly one outcome.
Another term frequently used in probability is a random "event." A random event is a higher level outcome that may depend on multiple experiments and multiple outcomes of the experiments. For example, consider a game consisting of two random experiments, "throwing a die" and "throwing a coin." A player is to throw the die twice and the coin once. A player who gets the face with one spot in both die-throwings and a "head" in the coin-throwing wins the grand prize. In this game, the random "event" of interest is "winning the grand prize." This event would "occur," if the trials produce the following outcomes: one spot in both of the die-throwings and a "head" in the coin-throwing. In this example, the event depends on multiple experiments and multiple...
