**Probability of Picking 3 Blue Marbles** **Problem Statement:** A bag contains 7 red, 3 white, and 9 blue marbles. Find the probability of picking 3 blue marbles if each marble is returned to the bag before the next marble is picked. **Options:** - 729/6859 - 9/19 - 1/3 - 1/6859 **Submit Question:** This is a multiple-choice question where you are required to select one of the options and click "Submit Question" to record your answer. **Explanation:** In this scenario of probability with replacement, the total number of marbles (7 red + 3 white + 9 blue) is 19. The probability of picking a blue marble in one draw is the number of blue marbles (9) divided by the total number of marbles (19), or 9/19. Since each marble is replaced after drawing, the probability remains the same for each draw. Thus, the probability of drawing 3 blue marbles in succession is: \[ \left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) = \left(\frac{9}{19}\right)^3 = \frac{729}{6859} \]
**Probability of Picking 3 Blue Marbles** **Problem Statement:** A bag contains 7 red, 3 white, and 9 blue marbles. Find the probability of picking 3 blue marbles if each marble is returned to the bag before the next marble is picked. **Options:** - 729/6859 - 9/19 - 1/3 - 1/6859 **Submit Question:** This is a multiple-choice question where you are required to select one of the options and click "Submit Question" to record your answer. **Explanation:** In this scenario of probability with replacement, the total number of marbles (7 red + 3 white + 9 blue) is 19. The probability of picking a blue marble in one draw is the number of blue marbles (9) divided by the total number of marbles (19), or 9/19. Since each marble is replaced after drawing, the probability remains the same for each draw. Thus, the probability of drawing 3 blue marbles in succession is: \[ \left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) = \left(\frac{9}{19}\right)^3 = \frac{729}{6859} \]
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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Question
![**Probability of Picking 3 Blue Marbles**
**Problem Statement:**
A bag contains 7 red, 3 white, and 9 blue marbles. Find the probability of picking 3 blue marbles if each marble is returned to the bag before the next marble is picked.
**Options:**
- 729/6859
- 9/19
- 1/3
- 1/6859
**Submit Question:**
This is a multiple-choice question where you are required to select one of the options and click "Submit Question" to record your answer.
**Explanation:**
In this scenario of probability with replacement, the total number of marbles (7 red + 3 white + 9 blue) is 19. The probability of picking a blue marble in one draw is the number of blue marbles (9) divided by the total number of marbles (19), or 9/19. Since each marble is replaced after drawing, the probability remains the same for each draw.
Thus, the probability of drawing 3 blue marbles in succession is:
\[
\left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) = \left(\frac{9}{19}\right)^3 = \frac{729}{6859}
\]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F33614614-cd9e-4559-9a21-56f7eb77d3ea%2Fd88f79e2-6ffc-45c4-8e42-68dd8097bb5d%2F98dy21.jpeg&w=3840&q=75)
Transcribed Image Text:**Probability of Picking 3 Blue Marbles**
**Problem Statement:**
A bag contains 7 red, 3 white, and 9 blue marbles. Find the probability of picking 3 blue marbles if each marble is returned to the bag before the next marble is picked.
**Options:**
- 729/6859
- 9/19
- 1/3
- 1/6859
**Submit Question:**
This is a multiple-choice question where you are required to select one of the options and click "Submit Question" to record your answer.
**Explanation:**
In this scenario of probability with replacement, the total number of marbles (7 red + 3 white + 9 blue) is 19. The probability of picking a blue marble in one draw is the number of blue marbles (9) divided by the total number of marbles (19), or 9/19. Since each marble is replaced after drawing, the probability remains the same for each draw.
Thus, the probability of drawing 3 blue marbles in succession is:
\[
\left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) \times \left(\frac{9}{19}\right) = \left(\frac{9}{19}\right)^3 = \frac{729}{6859}
\]
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