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probability that the arrow will land on a region lettered C and then a G?

probability that the arrow will land on a region lettered C and then a G?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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This image features a multiple-choice question with four options, each having a fraction next to it. Here is the transcribed text for educational purposes: --- **Question:** Select the correct option for the given problem. **Options:** 1. \( \frac{1}{16} \) 2. \( \frac{1}{64} \) 3. \( \frac{1}{4} \) 4. \( \frac{1}{8} \) --- This layout represents a standard format seen in multiple-choice questions and tests. Each option is prefixed with a number followed by the corresponding fraction. This type of question is commonly used in mathematics education to assess understanding of fractions and their relative magnitudes.
Transcribed Image Text:This image features a multiple-choice question with four options, each having a fraction next to it. Here is the transcribed text for educational purposes: --- **Question:** Select the correct option for the given problem. **Options:** 1. \( \frac{1}{16} \) 2. \( \frac{1}{64} \) 3. \( \frac{1}{4} \) 4. \( \frac{1}{8} \) --- This layout represents a standard format seen in multiple-choice questions and tests. Each option is prefixed with a number followed by the corresponding fraction. This type of question is commonly used in mathematics education to assess understanding of fractions and their relative magnitudes.
**Educational Content on Probability and Spinners** **Understanding the Spinner:** In this exercise, we examine a spinner that is divided into eight equal regions. The spinner is used to understand basic probability concepts. **Spinner Description:** The spinner is sectioned into eight equal parts, each labeled with a different letter: - A - B - C - D - E - F - G - H **Diagram Explanation:** The diagram displays a circular spinner divided into 8 equal slices, each labeled from A to H in a clockwise direction. An arrow in the center points towards the edge of the circle, indicating the result of each spin. **Probability Question:** The question presented is: "If Rob spins the spinner twice, what is the probability that the arrow will land on a region lettered 'C' and then on a region lettered 'G'?" **Solution:** 1. **Calculate the Probability for the First Spin (landing on 'C'):** - Since one out of the eight regions is labeled 'C': - Probability of landing on 'C' = 1/8 2. **Calculate the Probability for the Second Spin (landing on 'G'):** - Since one out of the eight regions is labeled 'G': - Probability of landing on 'G' = 1/8 3. **Determine the Combined Probability:** - Since both events (landing on 'C' and then 'G') are independent, the combined probability can be calculated by multiplying the probabilities of each event: - Combined Probability = Probability of first event x Probability of second event - Combined Probability = (1/8) x (1/8) - Combined Probability = 1/64 **Conclusion:** The probability that Rob will spin the spinner and land on 'C' first and then on 'G' in his second spin is 1/64. This demonstrates how probabilities are multiplied in independent events.
Transcribed Image Text:**Educational Content on Probability and Spinners** **Understanding the Spinner:** In this exercise, we examine a spinner that is divided into eight equal regions. The spinner is used to understand basic probability concepts. **Spinner Description:** The spinner is sectioned into eight equal parts, each labeled with a different letter: - A - B - C - D - E - F - G - H **Diagram Explanation:** The diagram displays a circular spinner divided into 8 equal slices, each labeled from A to H in a clockwise direction. An arrow in the center points towards the edge of the circle, indicating the result of each spin. **Probability Question:** The question presented is: "If Rob spins the spinner twice, what is the probability that the arrow will land on a region lettered 'C' and then on a region lettered 'G'?" **Solution:** 1. **Calculate the Probability for the First Spin (landing on 'C'):** - Since one out of the eight regions is labeled 'C': - Probability of landing on 'C' = 1/8 2. **Calculate the Probability for the Second Spin (landing on 'G'):** - Since one out of the eight regions is labeled 'G': - Probability of landing on 'G' = 1/8 3. **Determine the Combined Probability:** - Since both events (landing on 'C' and then 'G') are independent, the combined probability can be calculated by multiplying the probabilities of each event: - Combined Probability = Probability of first event x Probability of second event - Combined Probability = (1/8) x (1/8) - Combined Probability = 1/64 **Conclusion:** The probability that Rob will spin the spinner and land on 'C' first and then on 'G' in his second spin is 1/64. This demonstrates how probabilities are multiplied in independent events.
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