ew recruits at the Ŝac in one of six platoons Farmers. The probat all platoons. ability that Edward is
ew recruits at the Ŝac in one of six platoons Farmers. The probat all platoons. ability that Edward is
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...
Related questions
Concept explainers
Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
Linear Functions
A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
![### Section 11 – Topic 4
## Probability and the Addition Rule – Part 2
1. **Noah and Edward** are new recruits at the **Sacagawea Tracking Training Ground** and are placed in one of six platoons: Colonials, Pilgrims, Sioux, Creek, Prospectors, and Farmers. The probability of being put into a platoon is equal among all platoons.
**Part A:** What is the probability that Edward is assigned to the Sioux platoon?
**Part B:** What is the probability that Noah is not part of the Prospectors or the Farmers platoons?
**Part C:** What is the probability that Edward and Noah are assigned to the Pilgrim platoon?
**Part D:** What is the probability that both Edward and Noah are part of the Colonials platoon?
2. Assume the events are independent of each other and use the principles of probability and addition rules to solve the problems. An explanation of the methodology can be given with relevant formulas and conditional probabilities if required.
#### Explanation:
**Part A Explanation:**
The probability of Edward being assigned to the Sioux platoon is calculated as:
\[ P(E_{\text{Sioux}}) = \frac{1}{6} \]
**Part B Explanation:**
The probability that Noah is not part of the Prospectors or the Farmers platoons is calculated as:
\[ P(N_{\text{not Prospectors or Farmers}}) = 1 - P(N_{\text{Prospectors}}) - P(N_{\text{Farmers}}) \]
\[ P(N_{\text{not Prospectors or Farmers}}) = 1 - \frac{1}{6} - \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \]
**Part C Explanation:**
The probability that Edward and Noah are assigned to the Pilgrim platoon independently:
\[ P(E_{\text{Pilgrim}} \text{ and } N_{\text{Pilgrim}}) = P(E_{\text{Pilgrim}}) \times P(N_{\text{Pilgrim}}) = \left(\frac{1}{6}\right) \times \left(\frac{1}{6}\right) = \frac{1}{36} \]
**Part D Explanation:**
The probability that both Edward and Noah are part of the Colonials platoon independently:
\[](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe5ed07d5-7a8f-4097-9c81-82df457ca627%2F069f754d-db93-45c1-968d-763b356bc5b3%2Feqwnubs_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Section 11 – Topic 4
## Probability and the Addition Rule – Part 2
1. **Noah and Edward** are new recruits at the **Sacagawea Tracking Training Ground** and are placed in one of six platoons: Colonials, Pilgrims, Sioux, Creek, Prospectors, and Farmers. The probability of being put into a platoon is equal among all platoons.
**Part A:** What is the probability that Edward is assigned to the Sioux platoon?
**Part B:** What is the probability that Noah is not part of the Prospectors or the Farmers platoons?
**Part C:** What is the probability that Edward and Noah are assigned to the Pilgrim platoon?
**Part D:** What is the probability that both Edward and Noah are part of the Colonials platoon?
2. Assume the events are independent of each other and use the principles of probability and addition rules to solve the problems. An explanation of the methodology can be given with relevant formulas and conditional probabilities if required.
#### Explanation:
**Part A Explanation:**
The probability of Edward being assigned to the Sioux platoon is calculated as:
\[ P(E_{\text{Sioux}}) = \frac{1}{6} \]
**Part B Explanation:**
The probability that Noah is not part of the Prospectors or the Farmers platoons is calculated as:
\[ P(N_{\text{not Prospectors or Farmers}}) = 1 - P(N_{\text{Prospectors}}) - P(N_{\text{Farmers}}) \]
\[ P(N_{\text{not Prospectors or Farmers}}) = 1 - \frac{1}{6} - \frac{1}{6} = \frac{4}{6} = \frac{2}{3} \]
**Part C Explanation:**
The probability that Edward and Noah are assigned to the Pilgrim platoon independently:
\[ P(E_{\text{Pilgrim}} \text{ and } N_{\text{Pilgrim}}) = P(E_{\text{Pilgrim}}) \times P(N_{\text{Pilgrim}}) = \left(\frac{1}{6}\right) \times \left(\frac{1}{6}\right) = \frac{1}{36} \]
**Part D Explanation:**
The probability that both Edward and Noah are part of the Colonials platoon independently:
\[
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 2 steps with 2 images
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, probability and related others by exploring similar questions and additional content below.Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON