Textbook Question
Finding the Probability of the Complement of an Event In Exercises 17-20, the probability that an event will happen is given. Find the probability that the event will not happen.
19. P(E)=0.03
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Ch. 3 - Probability
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470
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Table of contents
- Ch. 1 - Introduction to Statistics87
- Ch. 2 - Descriptive Statistics176
- Ch. 3 - Probability184
- Ch. 4 - Discrete Probability Distributions102
- Ch. 5 - Normal Probability Distributions183
- Ch. 6 - Confidence Intervals154
- Ch. 7 - Hypothesis Testing with One Sample165
- Ch. 8 - Hypothesis Testing with Two Samples134
- Ch. 9 - Correlation and Regression87
- Ch. 10 - Chi-Square Tests and the F-Distribution87
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
Chapter 3, Problem 3.1.90
Writing In Exercises 89 and 90, write a statement that represents the complement of the probability.
90. The probability of randomly choosing a car with more than one cause for showing its "CHECK ENGINE" light from the population of vehicles showing "CHECK ENGINE" lights.
Verified step by step guidance1
Understand the concept of complement probability: The complement of a probability is the likelihood of the opposite event occurring. If the probability of an event is P(A), the complement is calculated as 1 - P(A).
Identify the event in the problem: The event described is 'randomly choosing a car with more than one cause for showing its "CHECK ENGINE" light.'
Define the complement event: The complement of this event is 'randomly choosing a car with one or no cause for showing its "CHECK ENGINE" light.'
Write the mathematical representation: Let P(A) represent the probability of choosing a car with more than one cause for showing its "CHECK ENGINE" light. The complement probability is represented as P(A') = 1 - P(A).
Express the statement clearly: The complement probability is the likelihood of randomly choosing a car with one or no cause for showing its "CHECK ENGINE" light, which is calculated as 1 minus the probability of choosing a car with more than one cause.
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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. A probability of 0 indicates that the event cannot happen, while a probability of 1 indicates certainty. In this context, it refers to the chance of selecting a car with specific characteristics from a defined population.
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Complement of Probability
The complement of a probability event is the probability that the event does not occur. It is calculated as 1 minus the probability of the event. For example, if the probability of choosing a car with more than one cause for the 'CHECK ENGINE' light is P, then the complement would be 1 - P, representing the probability of choosing a car without that characteristic.
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Population and Sample
In statistics, a population refers to the entire group of individuals or items that we are interested in studying, while a sample is a subset of that population. In this question, the population consists of all vehicles showing 'CHECK ENGINE' lights, and understanding this distinction is crucial for accurately interpreting probabilities related to specific characteristics within that group.
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Related Practice
Textbook Question
Finding the Probability of an Event In Exercises 21-24, the probability that an event will not happen is given. Find the probability that the event will happen.
21. P(E') =0.95
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Textbook Question
"Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.
9. Selecting a king from a standard deck of 52 playing cards, replacing it, and then selecting a queen from the deck"
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Textbook Question
Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.
14. A ball is selected from a bin of balls numbered from 1 through 52. It is replaced, and then a second numbered ball is selected from the bin.
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Textbook Question
Board of Directors The University of Colorado Board of Directors has 23 members. One member serves as board chair and another serves as vice chair. Given the names of the 23
board members, what is the probability of randomly selecting the name of the chair and the name of the vice chair? (Source: University of Colorado)
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Textbook Question
37. Water Pollution An environmental agency is analyzing water samples from 80 lakes for pollution. Five of the lakes have dangerously high levels of dioxin. Six lakes are randomly selected from the sample. Use technology to find how many ways one polluted lake and five nonpolluted lakes can be chosen.
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