Use the spinner shown. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability that it will land on green and then green. Q Find the probability that the spinner will land on green and then green. The probability is (Type an integer or a simplified fraction.)
Use the spinner shown. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability that it will land on green and then green. Q Find the probability that the spinner will land on green and then green. The probability is (Type an integer or a simplified fraction.)
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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![**Spinner Probability Exercise**
*Description:*
The image shows a spinner divided into six equal sections, each labeled with a color: Red, Yellow, and Green. The sections are arranged as follows: Green, Red, Yellow, Green, Red, and Yellow.
*Instructions:*
Use the spinner shown. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability that it will land on green and then green.
*Task:*
Find the probability that the spinner will land on green and then green.
*Solution Steps:*
1. **Calculate the Probability for the First Spin**:
The spinner has two green sections out of six total sections. Therefore, the probability that the pointer will land on green during the first spin is \( \frac{2}{6} \) or \( \frac{1}{3} \).
2. **Calculate the Probability for the Second Spin**:
Assuming the pointer lands on green in the first spin, the probability that it will land on green again during the second spin is also \( \frac{1}{3} \), as each spin is an independent event.
3. **Combine Probabilities**:
To find the total probability for both events (landing on green twice in a row), multiply the probabilities of each independent event:
\[
\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
*Answer:*
The probability is \( \frac{1}{9} \).
(Type your answer as an integer or a simplified fraction.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb8a8da77-9f04-4511-b9d9-b7e746f1af1d%2Fc4f3156a-40f2-489e-ae09-97023106230e%2Fpdy2dba_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Spinner Probability Exercise**
*Description:*
The image shows a spinner divided into six equal sections, each labeled with a color: Red, Yellow, and Green. The sections are arranged as follows: Green, Red, Yellow, Green, Red, and Yellow.
*Instructions:*
Use the spinner shown. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability that it will land on green and then green.
*Task:*
Find the probability that the spinner will land on green and then green.
*Solution Steps:*
1. **Calculate the Probability for the First Spin**:
The spinner has two green sections out of six total sections. Therefore, the probability that the pointer will land on green during the first spin is \( \frac{2}{6} \) or \( \frac{1}{3} \).
2. **Calculate the Probability for the Second Spin**:
Assuming the pointer lands on green in the first spin, the probability that it will land on green again during the second spin is also \( \frac{1}{3} \), as each spin is an independent event.
3. **Combine Probabilities**:
To find the total probability for both events (landing on green twice in a row), multiply the probabilities of each independent event:
\[
\frac{1}{3} \times \frac{1}{3} = \frac{1}{9}
\]
*Answer:*
The probability is \( \frac{1}{9} \).
(Type your answer as an integer or a simplified fraction.)
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