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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 3.2.17
Chapter 3, Problem 3.2.17

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.
17. A study found that there is no relationship between playing violent video games and aggressive or bullying behavior in teenagers. (Source: The Royal Society Publishing)

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Identify the two events described in the study. In this case, the two events are: (1) playing violent video games and (2) exhibiting aggressive or bullying behavior in teenagers.
Understand the concept of independence in probability. Two events are independent if the occurrence of one event does not affect the probability of the occurrence of the other event.
Analyze the study's findings. The study states that there is no relationship between playing violent video games and aggressive or bullying behavior. This suggests that the probability of one event occurring is not influenced by the other.
Conclude that the events are independent based on the study's findings. Since the study explicitly states there is no relationship, the events do not affect each other.
Explain the reasoning. Independence is determined by the lack of a causal or statistical relationship between the two events, as indicated by the study's results.

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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 occurrence does not affect the probability of the occurrence of another event. In probability theory, two events A and B are independent if the probability of both occurring together is equal to the product of their individual probabilities, P(A and B) = P(A) * P(B). Understanding this concept is crucial for determining whether the results of a study suggest a relationship between the events being analyzed.
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Dependent Events

Dependent events are events where the occurrence of one event affects the probability of the other event occurring. For example, if event A influences the likelihood of event B, then they are considered dependent. In the context of the study mentioned, if playing violent video games were found to influence aggressive behavior, the two events would be dependent, indicating a relationship between them.
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Probability of Multiple Independent Events

Statistical Significance

Statistical significance refers to the likelihood that a relationship between two or more variables is caused by something other than mere chance. In studies, researchers often use p-values to determine significance, with a common threshold being p < 0.05. In the context of the study on video games and aggression, finding no significant relationship suggests that any observed effects are likely due to random variation rather than a true causal link.
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Related Practice
Textbook Question

According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is

P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

33. P(A) = 2/3, P(A') = 1/3, P(B|A) = 1/5 , and P(B|A') = 1/2

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Textbook Question

"According to Bayes’ Theorem, the probability of event A , given that event B has occurred, is

P(A|B) = P(A) * P(B|A)P(A) * P(B|A) + P(A') * P(B|A').

In Exercises 33–38, use Bayes’ Theorem to find P(A|B).

35. P(A) = 0.25, P(A') = 0.75, P(B|A) = 0.3 , and P(B|A') = 0.5 "

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Textbook Question

1. When two events are mutually exclusive, why is P(A and B) = 0?

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Textbook Question

True or False? In Exercises 3-6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

3. A combination is an ordered arrangement of objects.

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Textbook Question

Matching Probabilities In Exercises 11-16, match the event with its probability.

a. 0.95

b. 0.005

c. 0.25

d. 0

e. 0.375

f. 0.5

11. A random number generator is used to select a number from 1 to 100. What is the probability of selecting the number 153?

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Textbook Question

Cards In Exercises 59-62, you are dealt a hand of five cards from a standard deck of 52 playing cards.

59. Find the probability of being dealt two clubs and one of each of the other three suits.

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