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Ch. 3 - Probability
Larson - Elementary Statistics: Picturing the World 8th Edition
Larson8th EditionElementary Statistics: Picturing the WorldISBN: 9780137493470Not the one you use?Change textbook
All textbooksLarson 8th EditionCh. 3 - ProbabilityProblem 3.2.2
Chapter 3, Problem 3.2.2

"2. Give an example of
a. two events that are independent.
b. two events that are dependent."

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1
Understand the concept of independent events: Two events are independent if the occurrence of one event does not affect the probability of the other event. Mathematically, events A and B are independent if P(A ∩ B) = P(A) * P(B).
Understand the concept of dependent events: Two events are dependent if the occurrence of one event affects the probability of the other event. For example, if event A occurs, it changes the likelihood of event B occurring.
For part (a), think of two events that do not influence each other. For example, flipping a coin and rolling a die are independent events because the outcome of the coin flip does not affect the outcome of the die roll.
For part (b), think of two events where one affects the other. For example, drawing two cards from a deck without replacement is a dependent event because the outcome of the first draw changes the probabilities for the second draw.
Summarize your examples and verify that they align with the definitions of independence and dependence. Ensure that for independent events, P(A ∩ B) = P(A) * P(B), and for dependent events, the probabilities are influenced by the occurrence of one event.

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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 two or more events where the occurrence of one event does not affect the probability of the other event occurring. For example, flipping a coin and rolling a die are independent events; the outcome of the coin flip has no impact on the result of the die roll.
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Probability of Multiple Independent Events

Dependent Events

Dependent events are events where the occurrence of one event influences the probability of the other event occurring. For instance, drawing two cards from a deck without replacement is a dependent event; the outcome of the first draw affects the composition of the deck for the second draw.
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Multiplication Rule: Dependent Events

Probability

Probability is a measure of the likelihood that a particular event will occur, expressed as a number between 0 and 1. Understanding probability is essential for distinguishing between independent and dependent events, as it helps quantify how the occurrence of one event impacts the likelihood of another.
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Introduction to Probability
Related Practice
Textbook Question

1. When you calculate the number of permutations of n distinct objects taken r at a time, what are you counting? Give an example.

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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.

12. Not putting money in a parking meter and getting a parking ticket"

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)"

Textbook Question

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

Textbook Question

16. Can Defects Of the cans produced by a company, 96% do not have a puncture, 93% do not have a smashed edge, and 89.3% have neither a puncture nor a smashed edge. Find

the probability that a randomly selected can does not have a puncture or a smashed edge.

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