Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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![### Probability Question on Segment Selection
#### Problem Statement:
A point \( P \) is selected at random from segment \( AG \). What is the probability that \( P \) is on segment \( AD \)?
#### Diagram Explanation:
The diagram is a number line with labeled points and their corresponding positions:
- \( A \) at \(-3\)
- \( B \) at \(-2\)
- \( C \) at \(-1\)
- \( D \) at \(0\)
- \( E \) at \(1\)
- \( F \) at \(2\)
- \( G \) at \(3\)
The diagram shows a straight line with these points marked.
#### Answer Choices:
The possible probabilities are given as:
- a) \( 43\% \)
- b) \( 50\% \)
- c) \( 57\% \)
- d) \( 67\% \)
When working through this problem, note that:
- Segment \( AG \) spans from \( -3 \) to \( 3 \), giving a total segment length of \( 6 \).
- Segment \( AD \) spans from \( -3 \) to \( 0 \), giving a segment length of \( 3 \).
To find the probability that \( P \) is on segment \( AD \), we calculate:
\[ \text{Probability} = \frac{\text{Length of segment } AD}{\text{Length of segment } AG} = \frac{3}{6} = \frac{1}{2} = 50\% \]
#### Correct Answer:
- b) \( 50\% \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F74ca1d37-d294-4f01-9907-950537ec9baa%2F83ed16d5-7bfc-44af-bb75-abd527ad926c%2Fkv6jl7_processed.png&w=3840&q=75)
Transcribed Image Text:### Probability Question on Segment Selection
#### Problem Statement:
A point \( P \) is selected at random from segment \( AG \). What is the probability that \( P \) is on segment \( AD \)?
#### Diagram Explanation:
The diagram is a number line with labeled points and their corresponding positions:
- \( A \) at \(-3\)
- \( B \) at \(-2\)
- \( C \) at \(-1\)
- \( D \) at \(0\)
- \( E \) at \(1\)
- \( F \) at \(2\)
- \( G \) at \(3\)
The diagram shows a straight line with these points marked.
#### Answer Choices:
The possible probabilities are given as:
- a) \( 43\% \)
- b) \( 50\% \)
- c) \( 57\% \)
- d) \( 67\% \)
When working through this problem, note that:
- Segment \( AG \) spans from \( -3 \) to \( 3 \), giving a total segment length of \( 6 \).
- Segment \( AD \) spans from \( -3 \) to \( 0 \), giving a segment length of \( 3 \).
To find the probability that \( P \) is on segment \( AD \), we calculate:
\[ \text{Probability} = \frac{\text{Length of segment } AD}{\text{Length of segment } AG} = \frac{3}{6} = \frac{1}{2} = 50\% \]
#### Correct Answer:
- b) \( 50\% \)
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