A bag contains 8 yellow marbles, 7 white marbles, 6 green marbles. If one marble is drawn from the bag then replaced, what is the probability of drawing a yellow marble then a green marble? In a number guessing game. You ask a person to guess a number from one 1 to 10. If the person makes a random guess, what is the probability their guess will be less than 9? A bag contains 7 red marbles, 6 green marbles, 8 white marbles. If one marble is drawn from the bag but not replaced, what is the probability of drawing a red marble then a white marble?
A bag contains 8 yellow marbles, 7 white marbles, 6 green marbles. If one marble is drawn from the bag then replaced, what is the probability of drawing a yellow marble then a green marble? In a number guessing game. You ask a person to guess a number from one 1 to 10. If the person makes a random guess, what is the probability their guess will be less than 9? A bag contains 7 red marbles, 6 green marbles, 8 white marbles. If one marble is drawn from the bag but not replaced, what is the probability of drawing a red marble then a white marble?
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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![**Marble Probabilities and Number Guessing Game: Understanding Probability**
1. **Marble Probability Question 1: Replacement Scenario**
A bag contains 8 *yellow* marbles, 7 *white* marbles, and 6 *green* marbles.
- **Question:** If one marble is drawn from the bag and then replaced, what is the probability of drawing a *yellow* marble and then a *green* marble?
- **Explanation:** For this scenario, calculate the probability of two independent events: drawing a yellow marble and then a green marble. Since the marble is replaced between draws, each draw is independent.
\[ P(yellow) = \frac{8}{21} \]
\[ P(green) = \frac{6}{21} \]
\[ P(yellow \text{ then } green) = P(yellow) \times P(green) = \frac{8}{21} \times \frac{6}{21} \]
2. **Number Guessing Game: Range Probability**
- **Scenario:** In a number guessing game, a person guesses a number from 1 to 10.
- **Question:** What is the probability their guess will be less than 9?
- **Explanation:** Calculate the probability of guessing numbers 1 through 8.
\[ P(<9) = \frac{8}{10} = \frac{4}{5} \]
3. **Marble Probability Question 2: Without Replacement Scenario**
A bag contains 7 *red* marbles, 6 *green* marbles, and 8 *white* marbles.
- **Question:** If one marble is drawn from the bag but not replaced, what is the probability of drawing a *red* marble and then a *white* marble?
- **Explanation:** For this scenario, calculate the probability of two dependent events: drawing a red marble and then a white marble, with no replacement in between.
\[ P(red) = \frac{7}{21} \]
After one red marble is drawn, the total number of marbles is 20.
\[ P(white | red) = \frac{8}{20} \]
\[ P(red \text{ then } white) = P(red) \times P(white | red](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3911c819-e187-49b9-9fcc-b89884a563f1%2F72aceaa1-9c8c-4252-bee2-2ba9ec337d47%2F6133lh_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Marble Probabilities and Number Guessing Game: Understanding Probability**
1. **Marble Probability Question 1: Replacement Scenario**
A bag contains 8 *yellow* marbles, 7 *white* marbles, and 6 *green* marbles.
- **Question:** If one marble is drawn from the bag and then replaced, what is the probability of drawing a *yellow* marble and then a *green* marble?
- **Explanation:** For this scenario, calculate the probability of two independent events: drawing a yellow marble and then a green marble. Since the marble is replaced between draws, each draw is independent.
\[ P(yellow) = \frac{8}{21} \]
\[ P(green) = \frac{6}{21} \]
\[ P(yellow \text{ then } green) = P(yellow) \times P(green) = \frac{8}{21} \times \frac{6}{21} \]
2. **Number Guessing Game: Range Probability**
- **Scenario:** In a number guessing game, a person guesses a number from 1 to 10.
- **Question:** What is the probability their guess will be less than 9?
- **Explanation:** Calculate the probability of guessing numbers 1 through 8.
\[ P(<9) = \frac{8}{10} = \frac{4}{5} \]
3. **Marble Probability Question 2: Without Replacement Scenario**
A bag contains 7 *red* marbles, 6 *green* marbles, and 8 *white* marbles.
- **Question:** If one marble is drawn from the bag but not replaced, what is the probability of drawing a *red* marble and then a *white* marble?
- **Explanation:** For this scenario, calculate the probability of two dependent events: drawing a red marble and then a white marble, with no replacement in between.
\[ P(red) = \frac{7}{21} \]
After one red marble is drawn, the total number of marbles is 20.
\[ P(white | red) = \frac{8}{20} \]
\[ P(red \text{ then } white) = P(red) \times P(white | red
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