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Find the probability that a point on SK is not on PK. Answer as a fraction in simplist form. TH P. R K -10-8 -4 -2 0 2 4. 6. 8. 10

Find the probability that a point on SK is not on PK. Answer as a fraction in simplist form. TH P. R K -10-8 -4 -2 0 2 4. 6. 8. 10

Elementary Geometry For College Students, 7e
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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**Geometry: Second Semester Exam** **Question 5:** Find the probability that a point on \( \overline{SK} \) is not on \( \overline{PK} \). Answer as a fraction in simplest form. **Diagram Explanation:** The diagram is a number line with labeled points: - \( S \) at -10 - \( T \) at -2 - \( H \) at 0 - \( P \) at 4 - \( R \) at 8 - \( K \) at 10 The number line goes from -10 to 10 with the points \( S \), \( T \), \( H \), \( P \), \( R \), and \( K \) marked as indicated. You are asked to find the probability that a random point chosen on the line segment \( \overline{SK} \) (from \( S \) at -10 to \( K \) at 10) does not lie on \( \overline{PK} \) (from \( P \) at 4 to \( K \) at 10). To solve the problem: 1. Calculate the total length of \( \overline{SK} \). 2. Calculate the length of \( \overline{PK} \). 3. Subtract the length of \( \overline{PK} \) from the total length of \( \overline{SK} \) to find the length that is not on \( \overline{PK} \). 4. Find the probability by dividing the length not on \( \overline{PK} \) by the total length of \( \overline{SK} \). Calculation steps: 1. Length of \( \overline{SK} \) = \( K - S = 10 - (-10) = 20 \) 2. Length of \( \overline{PK} \) = \( K - P = 10 - 4 = 6 \) 3. Length not on \( \overline{PK} \) = \( 20 - 6 = 14 \) Probability = \( \frac{14}{20} = \frac{7}{10} \) So, the probability that a point on \( \overline{SK} \) is not on \( \overline{PK} \) is \( \frac{7}{10} \).
Transcribed Image Text:**Geometry: Second Semester Exam** **Question 5:** Find the probability that a point on \( \overline{SK} \) is not on \( \overline{PK} \). Answer as a fraction in simplest form. **Diagram Explanation:** The diagram is a number line with labeled points: - \( S \) at -10 - \( T \) at -2 - \( H \) at 0 - \( P \) at 4 - \( R \) at 8 - \( K \) at 10 The number line goes from -10 to 10 with the points \( S \), \( T \), \( H \), \( P \), \( R \), and \( K \) marked as indicated. You are asked to find the probability that a random point chosen on the line segment \( \overline{SK} \) (from \( S \) at -10 to \( K \) at 10) does not lie on \( \overline{PK} \) (from \( P \) at 4 to \( K \) at 10). To solve the problem: 1. Calculate the total length of \( \overline{SK} \). 2. Calculate the length of \( \overline{PK} \). 3. Subtract the length of \( \overline{PK} \) from the total length of \( \overline{SK} \) to find the length that is not on \( \overline{PK} \). 4. Find the probability by dividing the length not on \( \overline{PK} \) by the total length of \( \overline{SK} \). Calculation steps: 1. Length of \( \overline{SK} \) = \( K - S = 10 - (-10) = 20 \) 2. Length of \( \overline{PK} \) = \( K - P = 10 - 4 = 6 \) 3. Length not on \( \overline{PK} \) = \( 20 - 6 = 14 \) Probability = \( \frac{14}{20} = \frac{7}{10} \) So, the probability that a point on \( \overline{SK} \) is not on \( \overline{PK} \) is \( \frac{7}{10} \).
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