PROBABILITY AND STATISTICS

The probability of an event is the likelihood that it will happen. Probabilities range between 0 (the event will never happen) and 1 (the event will always happen). When probability is unknown or a variable, it is typically represented as p. In some cases probabilities can be determined analytically by considering the range of possible outcomes for an event and their relative likelihoods. For instance, a throw of a fair six-sided die has six possible outcomes, each equally likely, resulting in a probability of 1/6 for any given number being thrown. Other probabilities must be estimated empirically, by repeatedly measuring outcomes of the event over a large number of trials. For instance, in baseball, players’ batting averages are empirical estimates of their likelihood of getting a hit when at bat.

The outcomes discussed so far are discrete: they have fixed, countable numbers of outcomes. For instance, a throw of a die has only six possible outcomes;...