Concept explainers
To calculate:
The expected value of given dart game.
Answer to Problem 12PPS
The expected value of given dart game is
Explanation of Solution
Given information:
In this,
Blue color has value
White color has value
Red color has value
Calculation:
A dartboard consists of
The center red circle has a radius of
The area of a circle is equal to
where,
Now, calculate the probability of the white region of the circle being hit by a dart.
Now calculate the probability of the blue region of the circle being hit by a dart.
The total probability the red region of the circle being hit by a dart was found to be
Now calculate the expected value of the dartboard by adding the products of the probabilities and corresponding point value.
To simulate the dartboard, generate random integers that correspond to each of the probabilities found for each region of the dartboard. Run
The frequency of outcomes will vary between sets of
Outcome | Frequency |
Red | |
Blue | |
White | |
Total |
Calculate the average value of the dartboard by adding the products of the simulated probabilities and the corresponding point values.
Chapter 13 Solutions
Geometry, Student Edition
Additional Math Textbook Solutions
College Algebra (7th Edition)
A First Course in Probability (10th Edition)
Thinking Mathematically (7th Edition)
- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning