13.7 Probability

Residents of the Southeastern United States are all too familiar with charts, known as spaghetti models, such as the one in [link] . They combine a collection of weather data to predict the most likely path of a hurricane. Each colored line represents one possible path. The group of squiggly lines can begin to resemble strands of spaghetti, hence the name. In this section, we will investigate methods for making these types of predictions.

Constructing probability models

Suppose we roll a six-sided number cube. Rolling a number cube is an example of an experiment    , or an activity with an observable result. The numbers on the cube are possible results, or outcomes    , of this experiment. The set of all possible outcomes of an experiment is called the sample space    of the experiment. The sample space for this experiment is $\left\{1,2,3,4,5,6\right\}.$ An event    is any subset of a sample space.

The likelihood of an event is known as probability    . The probability of an event $p$ is a number that always satisfies $0\le p\le 1,$ where 0 indicates an impossible event and 1 indicates a certain event. A probability model    is a mathematical description of an experiment listing all possible outcomes and their associated probabilities. For instance, if there is a 1% chance of winning a raffle and a 99% chance of losing the raffle, a probability model would look much like [link] .

The sum of the probabilities listed in a probability model must equal 1, or 100%.