Textbook Question
"2. Give an example of
a. two events that are independent.
b. two events that are dependent."
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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 3.2.11
Classifying Events as Independent or Dependent In Exercises 9-14, determine whether the events are independent or dependent. Explain your reasoning.
11. Returning a rented movie after the due date and receiving a late fee
Verified step by step guidance1
Understand the definition of independent and dependent events: Independent events are those where the occurrence of one event does not affect the probability of the other. Dependent events are those where the occurrence of one event affects the probability of the other.
Identify the two events in the problem: Event A is 'returning a rented movie after the due date,' and Event B is 'receiving a late fee.'
Analyze the relationship between the two events: Consider whether Event A (returning the movie late) influences the likelihood of Event B (receiving a late fee).
Determine if the events are dependent: If returning the movie late directly causes or increases the likelihood of receiving a late fee, then the events are dependent. If there is no such relationship, they would be independent.
Conclude and explain: Based on the analysis, classify the events as dependent or independent and provide reasoning. For example, if returning the movie late directly results in a late fee, the events are dependent because one event affects the outcome of the other.
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Independent Events
Independent events are those whose outcomes do not affect each other. In probability, two events A and B are independent if the occurrence of A does not change the likelihood of B occurring, and vice versa. For example, flipping a coin and rolling a die are independent events because the result of one does not influence the other.
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Probability of Multiple Independent Events
Dependent Events
Dependent events are those where the outcome of one event affects the outcome of another. In probability, two events A and B are dependent if the occurrence of A changes the likelihood of B occurring. For instance, drawing cards from a deck without replacement is a classic example of dependent events, as the first draw affects the composition of the deck for the second draw.
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05:54Probability of Multiple Independent Events
Conditional Probability
Conditional probability refers to the probability of an event occurring given that another event has already occurred. It is denoted as P(A|B), which represents the probability of event A occurring given that event B has occurred. Understanding conditional probability is crucial for determining whether events are independent or dependent, as it helps to analyze how the occurrence of one event influences the likelihood of another.
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5:37Introduction to Probability
Related Practice
Textbook Question
13. Students A physics class has 40 students. Of these, 12 students are physics majors and 16 students are minoring in math. Of the physics majors, three are minoring in math. Find the probability that a randomly selected student is minoring in math or a physics major.
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Textbook Question
"Classifying Events Based on Studies In Exercises 15-18, identify the two events described in the study. Do the results indicate that the events are independent or dependent? Explain your reasoning.
15. A study was conducted to debunk the idea that abilities in music and math are related. Instead, the study showed a strong relationship between achievements in music and math.
(Source: University of Kansas)"
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Textbook Question
"Using the Multiplication Rule In Exercises 19-32, use the Multiplication Rule.
22.Pickup Trucks In a survey, 510 U.S. adults were asked whether they drive a pickup truck and whether they drive a Ford. The results showed that three in twenty adults surveyed drive a Ford. Of the adults surveyed that drive Fords, nine in twenty drive a pickup truck. Find the probability that a randomly selected adult drives a Ford and drives a pickup truck.
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Textbook Question
"Identifying the Sample Space of a Probability Experiment In Exercises 25-32, identify the sample space of the probability experiment and determine the number of outcomes in the sample space. Draw a tree diagram when appropriate.
26. Guessing a student's letter grade (A, B, C, D, F) in a class
"
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Textbook Question
True or False? In Exercises 7-10, determine whether the statement is true or false. If it is false, rewrite it as a true statement.
9. A probability of 1/10 indicates an unusual event.
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