The results of a restaurant survey are shown in the circle...

The results of a restaurant survey are shown in the circle graph with the measurement of each central angle. Each customer was asked to choose a favorite entrée. If a customer is chosen at random, find the probability of each response.
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neither pasta nor steak

Key Concepts

Complement Rule

The complement rule in probability is used to calculate the probability of an event not occurring by subtracting the probability of the event occurring from 1. In scenarios where the interest is in outcomes such as 'neither pasta nor steak', this rule helps compute the combined probability of all the remaining categories.

Probability as Relative Frequency

Probability as relative frequency involves determining the likelihood of an event by comparing the frequency (or proportion of the total) of that event's occurrence. In the context of a pie chart, the probability of a customer choosing a particular response is calculated by taking the fraction of the circle's angle (or percent) that corresponds to that category.

Circle Graph

A circle graph, or pie chart, is a visual representation of data where the whole circle represents the entirety of the dataset. Each sector or slice of the graph corresponds to a category, and its size is proportional to its frequency or percentage of the total. This type of graph is commonly used to represent proportions and make it easy to visualize parts of a whole.

Central Angle

In a circle graph, each sector’s central angle is directly proportional to the percentage or frequency of that category, since the entire circle measures 360 degrees. Calculating the proportion for a category involves dividing the measure of its central angle by 360 degrees. This approach helps convert the graphical representation into numerical probabilities.

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