Concept explainers
(a)
To construct: the probability model for this carnival game.
(a)
Explanation of Solution
Suppose that the random variable which shows the number of darts.
Denote the cases:
H = Hit the target
H’= Fail to hit the target
The associating probability of hitting the target and fail to hit the target are.
P(H) = 0.10
P(H’) = 0.90
Calculating the probability model for the carnival game.
A person willing to throw a dart in 4 time for $20.
So, X takes the values from 1 to 4. That is, X = 1, 2, 3, 4.
The probability of X=1 is, hitting the target by dart.
That is, P (X = 1) = 0.10
Then the probability would be:
The probability of X=3 can be written as, missing the first two darts and hitting by the third dart.
Then the probability would be:
similarly
Then the probability model for the carnival game would be
X | 1 | 2 | 3 | 4 |
P(X=x) | 0.10 | 0.90 | 0.081 | 0.729 |
(b)
To find: the expected number of darts that will throw.
(b)
Answer to Problem 6E
3.439
Explanation of Solution
Formula used:
Calculation:
Computer the expected number of darts that can be thrown
Hence, the expected number of darts that can be thrown is 3.439
(c)
To find: the expected winnings.
(c)
Answer to Problem 6E
17.197
Explanation of Solution
Formula used:
Calculation:
it costs to play $5 and if the person wins $100 they won’t return the $5.
Then the probability model becomes:
X | $95 | $90 | $85 | $80 | -$20 |
P(X=x) | 0.10 | 0.90 | 0.081 | 0.729 | 0.656 |
The expected winning is,
Therefore, the expected winning is 17.197.
Chapter 16 Solutions
Stats: Modeling the World Nasta Edition Grades 9-12
Additional Math Textbook Solutions
Statistics: The Art and Science of Learning from Data (4th Edition)
Elementary Statistics: Picturing the World (7th Edition)
Essentials of Statistics (6th Edition)
Statistics for Business and Economics (13th Edition)
Basic Business Statistics, Student Value Edition
Intro Stats, Books a la Carte Edition (5th Edition)
- MATLAB: An Introduction with ApplicationsStatisticsISBN:9781119256830Author:Amos GilatPublisher:John Wiley & Sons IncProbability and Statistics for Engineering and th...StatisticsISBN:9781305251809Author:Jay L. DevorePublisher:Cengage LearningStatistics for The Behavioral Sciences (MindTap C...StatisticsISBN:9781305504912Author:Frederick J Gravetter, Larry B. WallnauPublisher:Cengage Learning
- Elementary Statistics: Picturing the World (7th E...StatisticsISBN:9780134683416Author:Ron Larson, Betsy FarberPublisher:PEARSONThe Basic Practice of StatisticsStatisticsISBN:9781319042578Author:David S. Moore, William I. Notz, Michael A. FlignerPublisher:W. H. FreemanIntroduction to the Practice of StatisticsStatisticsISBN:9781319013387Author:David S. Moore, George P. McCabe, Bruce A. CraigPublisher:W. H. Freeman