Politics The responses of 1500 U.S. adults to a survey that asked them to state their own political viewpoints are shown in the Pareto chart. Find the probability of each event.(Adapted from YouGov)
d. Randomly selecting a person from the sample who is either unsure or moderate

Verified step by step guidance

1. Step 1: Understand the problem. The goal is to find the probability of randomly selecting a person from the sample who is either 'unsure' or 'moderate'. This involves adding the probabilities of these two categories.
2. Step 2: Identify the total number of respondents in the survey, which is given as 1500. This will serve as the denominator for calculating probabilities.
3. Step 3: From the Pareto chart, determine the number of respondents in the 'unsure' category and the 'moderate' category. These values will serve as the numerators for their respective probabilities.
4. Step 4: Add the counts of the 'unsure' and 'moderate' categories together to find the total number of respondents who fall into either of these two categories.
5. Step 5: Divide the total number of respondents in the 'unsure' or 'moderate' categories by the total number of respondents (1500) to calculate the probability. Use the formula: \( P(\text{unsure or moderate}) = \frac{\text{Number of unsure or moderate respondents}}{\text{Total respondents}} \).

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 involves calculating the chance of randomly selecting a person from a sample who falls into specific categories, such as 'unsure' or 'moderate' political viewpoints. Understanding how to compute probabilities based on survey data is essential for answering the question.

Pareto Chart

A Pareto chart is a type of bar graph that represents the frequency or impact of problems in a descending order, highlighting the most significant factors. In this case, the chart displays the political viewpoints of the surveyed individuals, allowing for a visual assessment of how many respondents identify as 'unsure' or 'moderate.' Familiarity with interpreting Pareto charts is crucial for extracting relevant data for probability calculations.

Sample Space

The sample space is the set of all possible outcomes in a probability experiment. For this question, it refers to the total number of respondents in the survey, which is 1500. Understanding the sample space is vital for calculating the probability of selecting individuals with specific characteristics, as it provides the denominator for probability calculations.