c) The student has competed in Smooth or Standard, but not Rhythm?Incorrect%d) The student has competed in Rhythm and Standard, but not Smooth?Incorrect%e) The student has competed in Rhythm. **Survey and Results: Ballroom Dance Studio Participation**A survey was conducted at a local ballroom dance studio to determine if students had ever competed in the following dance categories:- Smooth- Rhythm- StandardThe survey results were presented in a Venn Diagram as follows:- **Smooth only:** 4 students- **Rhythm only:** 8 students- **Standard only:** 11 students- **Smooth and Rhythm:** 6 students- **Smooth and Standard:** 7 students- **Rhythm and Standard:** 5 students- **All three categories (Smooth, Rhythm, Standard):** 15 students- **None of the categories:** 13 studentsThe Venn Diagram visually represents the overlap and distribution of students across these categories, enabling the dance studio owner to understand students' participation patterns.**Probability Calculation**The task is to calculate the probability of choosing a student at random from the surveyed group, and express this probability as a percentage rounded to the nearest tenth of a percent.

c) There are total (4+6+8+7+15+5+11+13)=69 The number of students that have competed in Smooth or Standard, but not Rhythm is=7 The probability that the student has competed in Smooth or Standard, but not Rhythm is: 769=0.101=10.1%d) There are total (4+6+8+7+15+5+11+13)=69 The number of students that have competed in Rhythm and Standard, but not Smooth is=5 The probability that the student has competed in Rhythm and Standard, but not Smooth=569=0.072=7.2% c) Total number of students in Rhythm is (6+8+15+5)=34 The probability that the student has competed in Rhythm is=3469=0.493=49.3% Answer(a): 10.1% Answer(b): 7.2% Answer(c): 49.3%

Math

Probability

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories: - Smooth Rhythm - Standard The results were then presented to the owner in the following Venn Diagram. Smooth Rhythm 4. 8 15 Standard 11 13 If a student is chosen at random, what is the probability that: Write your answers in percent form. Round to the nearest tenth of a percent.

A survey was conducted at a local ballroom dance studio asking students if they had ever competed in the following dance categories: - Smooth Rhythm - Standard The results were then presented to the owner in the following Venn Diagram. Smooth Rhythm 4. 8 15 Standard 11 13 If a student is chosen at random, what is the probability that: Write your answers in percent form. Round to the nearest tenth of a percent.

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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Concept explainers

Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

c) The student has competed in Smooth or Standard, but not Rhythm?Incorrect%
d) The student has competed in Rhythm and Standard, but not Smooth?Incorrect%
e) The student has competed in Rhythm.

**Survey and Results: Ballroom Dance Studio Participation**

A survey was conducted at a local ballroom dance studio to determine if students had ever competed in the following dance categories:
- Smooth
- Rhythm
- Standard

The survey results were presented in a Venn Diagram as follows:

- **Smooth only:** 4 students
- **Rhythm only:** 8 students
- **Standard only:** 11 students
- **Smooth and Rhythm:** 6 students
- **Smooth and Standard:** 7 students
- **Rhythm and Standard:** 5 students
- **All three categories (Smooth, Rhythm, Standard):** 15 students
- **None of the categories:** 13 students

The Venn Diagram visually represents the overlap and distribution of students across these categories, enabling the dance studio owner to understand students' participation patterns.

**Probability Calculation**

The task is to calculate the probability of choosing a student at random from the surveyed group, and express this probability as a percentage rounded to the nearest tenth of a percent.

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