Using the Fundamental Counting Principle In Exercises 37-40, use ...

4. Probability

Fundamental Counting Principle

Statistics

4. Probability

Fundamental Counting Principle

1:16 minutes

Problem 3.1.40

Textbook Question

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?

Verified step by step guidance

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.

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.

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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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?

Key Concepts

Fundamental Counting Principle

Binary Outcomes

Exponential Growth of Outcomes

Watch next

��app

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?