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A bag contains 4 red, 2 blue, 6 green, and 8 purple marbles. What is the probability of selecting a green marble at random from this bag, not replacing the marble, and then selecting another green marble? Round your answer to the nearest tenth of a percent if nece ssary

A bag contains 4 red, 2 blue, 6 green, and 8 purple marbles. What is the probability of selecting a green marble at random from this bag, not replacing the marble, and then selecting another green marble? Round your answer to the nearest tenth of a percent if nece ssary

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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The image illustrates a multiple-choice format typically seen in surveys or quizzes. It includes four options, each associated with a percentage value. Here is a transcription of the text and a detailed explanation of the elements present: **Multiple-Choice Options:** 1. ⃝ 60% 2. ⃝ 9.0% 3. ⃝ 12.6% 4. ⃝ 9.5% **Explanation:** Each line contains a circular selection button that participants can click to choose their answer, followed by the percentage value. The percentages listed are 60%, 9.0%, 12.6%, and 9.5%, respectively. This format is widely used in assessments, surveys, and educational quizzes to gauge participants' knowledge or opinions on various topics. The clear presentation of options allows for straightforward selection and response recording. There are no graphs or diagrams in the provided image. If an image of this nature were part of an educational content piece, it could be used, for example, to test knowledge on a particular subject matter involving statistical data or other quantitative information.
Transcribed Image Text:The image illustrates a multiple-choice format typically seen in surveys or quizzes. It includes four options, each associated with a percentage value. Here is a transcription of the text and a detailed explanation of the elements present: **Multiple-Choice Options:** 1. ⃝ 60% 2. ⃝ 9.0% 3. ⃝ 12.6% 4. ⃝ 9.5% **Explanation:** Each line contains a circular selection button that participants can click to choose their answer, followed by the percentage value. The percentages listed are 60%, 9.0%, 12.6%, and 9.5%, respectively. This format is widely used in assessments, surveys, and educational quizzes to gauge participants' knowledge or opinions on various topics. The clear presentation of options allows for straightforward selection and response recording. There are no graphs or diagrams in the provided image. If an image of this nature were part of an educational content piece, it could be used, for example, to test knowledge on a particular subject matter involving statistical data or other quantitative information.
**Probability Exercise: Selecting Green Marbles Without Replacement** **Problem Statement:** A bag contains a total number of marbles differentiated by colors as follows: - 4 red marbles - 2 blue marbles - 6 green marbles - 8 purple marbles **Question:** What is the probability of selecting a green marble at random from this bag, not replacing the marble, and then selecting another green marble? Round your answer to the nearest tenth of a percent if necessary. --- **Solution Steps:** 1. **Calculate the Total Number of Marbles:** - Total = 4 (red) + 2 (blue) + 6 (green) + 8 (purple) - Total = 20 marbles 2. **Probability of Selecting the First Green Marble:** - The number of green marbles = 6 - The probability of the first draw being green = \( \frac{6}{20} \) 3. **Calculate the New Total After One Green Marble is Removed:** - New total number of marbles = 20 - 1 = 19 - Remaining green marbles = 6 - 1 = 5 4. **Probability of Selecting the Second Green Marble (Without Replacement):** - The probability of the second draw being green = \( \frac{5}{19} \) 5. **Calculate the Combined Probability:** - The combined probability of both events happening = \( \frac{6}{20} \times \frac{5}{19} \) 6. **Simplify the Calculations:** - \( \frac{6}{20} = 0.3 \) - \( \frac{5}{19} \approx 0.2632 \) - Combined probability = \( 0.3 \times 0.2632 \approx 0.079 \) 7. **Convert to Percentage:** - \( 0.079 \times 100 \approx 7.9\% \) **Answer:** The probability of selecting a green marble first, not replacing it, and then selecting another green marble is approximately **7.9%**. **Note:** Always ensure to round the results to the nearest tenth of a percent if required.
Transcribed Image Text:**Probability Exercise: Selecting Green Marbles Without Replacement** **Problem Statement:** A bag contains a total number of marbles differentiated by colors as follows: - 4 red marbles - 2 blue marbles - 6 green marbles - 8 purple marbles **Question:** What is the probability of selecting a green marble at random from this bag, not replacing the marble, and then selecting another green marble? Round your answer to the nearest tenth of a percent if necessary. --- **Solution Steps:** 1. **Calculate the Total Number of Marbles:** - Total = 4 (red) + 2 (blue) + 6 (green) + 8 (purple) - Total = 20 marbles 2. **Probability of Selecting the First Green Marble:** - The number of green marbles = 6 - The probability of the first draw being green = \( \frac{6}{20} \) 3. **Calculate the New Total After One Green Marble is Removed:** - New total number of marbles = 20 - 1 = 19 - Remaining green marbles = 6 - 1 = 5 4. **Probability of Selecting the Second Green Marble (Without Replacement):** - The probability of the second draw being green = \( \frac{5}{19} \) 5. **Calculate the Combined Probability:** - The combined probability of both events happening = \( \frac{6}{20} \times \frac{5}{19} \) 6. **Simplify the Calculations:** - \( \frac{6}{20} = 0.3 \) - \( \frac{5}{19} \approx 0.2632 \) - Combined probability = \( 0.3 \times 0.2632 \approx 0.079 \) 7. **Convert to Percentage:** - \( 0.079 \times 100 \approx 7.9\% \) **Answer:** The probability of selecting a green marble first, not replacing it, and then selecting another green marble is approximately **7.9%**. **Note:** Always ensure to round the results to the nearest tenth of a percent if required.
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