1.2 Experimental Probability

When the outcomes of a random experiment are not equally-likely, the probability of any outcome or event can’t be determined theoretically. In these instances the probability can be estimated instead through repeated trials - this is referred to as the experimental probability. For example, if a motorist passes a set of traffic lights every morning and wishes to know the probability of having to wait at a red light on any given morning they could calculate the proportion of times they have to wait at a red light. If, over the course of 200 mornings, they have to wait at a red light 114 times

\[P(\text{red light})=\frac{114}{200}=\frac{57}{100}=0.57\]

The greater the number of trials used, the more likely it is that this proportion will accurately give the probability of the event. Generally, experimental probabilities should be considered less reliable than theoretical probabilities. However, many statisticians make valid use of experimental probabilities that have been obtained either by a sufficiently large number of observations or long-standing, historical knowledge of the probability of an event occuring.