4. Probability
Complements
2:11 minutesProblem 3.3.19c
Textbook Question
19. U.S. Age Distribution The projected percent distribution of the U.S. population for 2025 is shown in the pie chart. Find the probability of each event. (Source: U.S. Census
Bureau)
c. Randomly selecting someone who is not 60 years or over
Verified step by step guidance1
Step 1: Identify the age groups that are 60 years or over. From the pie chart, these groups are: 60–69 years (11.9%), 70–79 years (8.6%), and 80 years or older (4.5%).
Step 2: Add the percentages of these age groups to find the total percentage of the population that is 60 years or over. Use the formula: Total percentage = 11.9% + 8.6% + 4.5%.
Step 3: Subtract the total percentage of the population that is 60 years or over from 100% to find the percentage of the population that is not 60 years or over. Use the formula: Percentage not 60 years or over = 100% - Total percentage of 60 years or over.
Step 4: Convert the percentage of the population that is not 60 years or over into a probability. Since probability is expressed as a decimal, divide the percentage by 100. Use the formula: Probability = Percentage / 100.
Step 5: Interpret the result. The probability represents the likelihood of randomly selecting someone who is not 60 years or over from the U.S. population in 2025.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
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 involves calculating the chance of randomly selecting an individual from a specific age group based on the distribution percentages shown in the pie chart.
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Complementary Events
Complementary events are pairs of outcomes in probability that cover all possible outcomes of an experiment. For instance, in this question, selecting someone who is not 60 years or older is the complement of selecting someone who is 60 years or older, allowing for easier probability calculations.
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Pie Chart Interpretation
A pie chart visually represents data in a circular format, where each slice corresponds to a category's proportion of the whole. Understanding how to read the pie chart is crucial for determining the age distribution percentages, which are necessary for calculating the required probabilities.
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