A spinner consists of eight equal regions as shown. H. D F VE If Rob spins the spinner twice, what is the probability that the arrow will land on a region lettered C and then a G?
A spinner consists of eight equal regions as shown. H. D F VE If Rob spins the spinner twice, what is the probability that the arrow will land on a region lettered C and then a G?
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
Topic Video
Question
I am stuck on this question and I need help may you guys please help me with this
Thanks,
![### Understanding Probability in Spinner-based Games
**Concept Overview:**
A spinner consists of eight equal sections labeled A through H. Each segment represents an equal chance of the spinner landing on it when spun.
**Visual Representation:**
The diagram illustrates a spinner divided equally into eight parts, labeled as follows:
```
A B
H C
G D
--- E ---
F
```
**Problem Statement:**
Rob spins the spinner twice. The exercise asks to calculate the probability that the spinner will land on the section labeled "C" first and then on the section labeled "G" next.
**Calculation of Probability:**
To determine this, consider the following:
- Probability of landing on "C" in the first spin = 1/8 (since each of the 8 sections is equally likely).
- Probability of landing on "G" in the second spin = 1/8 (again, independently, each of the 8 sections is equally likely).
Therefore, the combined probability of landing on "C" in the first spin and "G" in the second spin is:
\[ \left( \frac{1}{8} \right) \times \left( \frac{1}{8} \right) = \frac{1}{64} \]
**Multiple-Choice Question:**
- What is the probability that Rob's spinner lands on regions "C" and "G" in sequence?
- \( \frac{1}{4} \)
- \( \frac{1}{64} \)
- \( 1 \) (Incorrect Answer Selection Highlighted)
- \( \frac{1}{8} \)
The correct answer is \( \frac{1}{64} \).
**Clarification:**
It's important to understand that each event (spin) is independent, hence the multiplication of their individual probabilities. This foundational concept is crucial for understanding combined probabilities in independent events.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcf2c3444-00a5-4cc6-af17-9e767d0389f2%2Fe4d1c4cf-bbe8-4945-956d-25800f2d83be%2Fub4g2b_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Understanding Probability in Spinner-based Games
**Concept Overview:**
A spinner consists of eight equal sections labeled A through H. Each segment represents an equal chance of the spinner landing on it when spun.
**Visual Representation:**
The diagram illustrates a spinner divided equally into eight parts, labeled as follows:
```
A B
H C
G D
--- E ---
F
```
**Problem Statement:**
Rob spins the spinner twice. The exercise asks to calculate the probability that the spinner will land on the section labeled "C" first and then on the section labeled "G" next.
**Calculation of Probability:**
To determine this, consider the following:
- Probability of landing on "C" in the first spin = 1/8 (since each of the 8 sections is equally likely).
- Probability of landing on "G" in the second spin = 1/8 (again, independently, each of the 8 sections is equally likely).
Therefore, the combined probability of landing on "C" in the first spin and "G" in the second spin is:
\[ \left( \frac{1}{8} \right) \times \left( \frac{1}{8} \right) = \frac{1}{64} \]
**Multiple-Choice Question:**
- What is the probability that Rob's spinner lands on regions "C" and "G" in sequence?
- \( \frac{1}{4} \)
- \( \frac{1}{64} \)
- \( 1 \) (Incorrect Answer Selection Highlighted)
- \( \frac{1}{8} \)
The correct answer is \( \frac{1}{64} \).
**Clarification:**
It's important to understand that each event (spin) is independent, hence the multiplication of their individual probabilities. This foundational concept is crucial for understanding combined probabilities in independent events.
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 3 steps with 3 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