Using a Pie Chart to Find Probabilities In Exercises 83-86, use the pie chart at the left, which shows the number of workers (in millions) by occupation for the United States. (Source: U.S. Bureau of Labor Statistics)
84. Find the probability that a worker chosen at random is not employed in a service occupation.

Verified step by step guidance

1. Step 1: Identify the total number of workers represented in the pie chart. To do this, sum up the values for all the occupational categories: 63.6 (Management, professional) + 29.7 (Sales, office) + 22.9 (Service) + 18.2 (Production, transportation, material moving) + 13.4 (Natural resources, construction, maintenance).
2. Step 2: Determine the number of workers employed in the 'Service' occupation. From the pie chart, this value is given as 22.9 million.
3. Step 3: Calculate the number of workers not employed in the 'Service' occupation. Subtract the number of workers in the 'Service' category from the total number of workers: Total workers - Workers in Service.
4. Step 4: Find the probability that a randomly chosen worker is not employed in the 'Service' occupation. This probability is calculated as the ratio of workers not in 'Service' to the total number of workers: (Workers not in Service) / (Total workers).
5. Step 5: Simplify the probability expression obtained in Step 4 to get the final probability value. Ensure the result is expressed as a decimal or fraction, depending on the context of the problem.

Key Concepts

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. In this context, it refers to the chance of randomly selecting a worker not employed in a service occupation. To calculate this, one must consider the total number of workers and the number of workers in service occupations.

Pie Chart

A pie chart is a circular statistical graphic divided into slices to illustrate numerical proportions. Each slice represents a category's contribution to the whole. In this case, the pie chart displays the distribution of workers across various occupations, allowing for a visual understanding of the proportion of workers in service versus other occupations.

Complementary Events

Complementary events are two outcomes of an event that are mutually exclusive and collectively exhaustive. In this scenario, the event of selecting a worker not in a service occupation is the complement of selecting a worker in a service occupation. Understanding this concept is crucial for calculating the probability of the desired outcome by subtracting the probability of the complementary event from 1.