A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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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.)](https://content.bartleby.com/qna-images/question/b8a8da77-9f04-4511-b9d9-b7e746f1af1d/c4f3156a-40f2-489e-ae09-97023106230e/pdy2dba_processed.jpeg)
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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