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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 3.1.40
Chapter 3, Problem 3.1.40

Using the Fundamental Counting Principle In Exercises 37-40, use the Fundamental Counting Principle.
40. True or False Quiz Assuming that no questions are left unanswered, in how many ways can a six-question true or false quiz be answered?

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Understand the Fundamental Counting Principle: This principle states that if one event can occur in 'm' ways and a second event can occur in 'n' ways, then the two events together can occur in m × n ways. Extend this to multiple events by multiplying the number of ways each event can occur.
Recognize that each question in the quiz is a binary choice (True or False). This means there are 2 possible answers for each question.
Identify the number of questions in the quiz, which is 6. Each question is an independent event, meaning the choice for one question does not affect the choices for the others.
Apply the Fundamental Counting Principle: Multiply the number of choices for each question (2) by itself for the total number of questions (6). This can be expressed mathematically as 2^6.
Conclude that the total number of ways to answer the quiz is given by the expression 2^6, which represents the total combinations of answers for the six questions.

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Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Fundamental Counting Principle

The Fundamental Counting Principle states that if there are 'n' ways to do one thing and 'm' ways to do another, then there are n × m ways to perform both actions. This principle is essential for calculating the total number of outcomes in scenarios where multiple independent choices are made.
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Fundamental Counting Principle

Binary Outcomes

In a true or false quiz, each question has two possible outcomes: true or false. This binary nature simplifies the application of the Fundamental Counting Principle, as each question can be treated as an independent event with two choices.
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Exponential Growth of Outcomes

When applying the Fundamental Counting Principle to a six-question true or false quiz, the total number of ways to answer the quiz can be calculated as 2 raised to the power of the number of questions (2^6). This illustrates how the number of outcomes grows exponentially with the number of questions.
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Related Practice
Textbook Question

20. Skating Eight people compete in a short track speed skating race. Assuming that there are no ties, in how many different orders can the skaters finish?

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Textbook Question

97. Rolling a Pair of Dice You roll a pair of six-sided dice and record the sum.

a. List all of the possible sums and determine the probability of rolling each sum.

b. Use technology to simulate rolling a pair of dice and record the sum 100 times. Make a tally of the 100 sums and use these results to list the probability of rolling

each sum.

c. Compare the probabilities in part (a) with the probabilities in part (b). Explain any similarities or differences.

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Textbook Question

Finding New Music In Exercises 45–48, use the pie chart, which shows the results of a survey of 513 music listeners who were asked about their primary source for new music. (Source: The Sound of AI)

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47. You choose nine music listeners at random. What is the probability that none of them say their primary source for new music is friends or social media?

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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).

34. P(A) = 3/8, P(A') = 5/8, P(B|A) = 2/3 , and P(B|A') = 3/5 "

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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.

6. 7C5=7C2

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Textbook Question

True or False? In Exercises 5 and 6, determine whether the statement is true or false. If it is false, rewrite it as a true statement.

6. If events A and B are dependent, then P(A and B) = P(A) · P(B).

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