Exercises 1-26 involve probabilities with independent events. Use the spinner shown to solve Exercises 1-10. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability it will land on If the pointer is spun three times, find the probability it will land on green every time.
Exercises 1-26 involve probabilities with independent events. Use the spinner shown to solve Exercises 1-10. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability it will land on If the pointer is spun three times, find the probability it will land on green every time.
Solution Summary: The author calculates the probability of occurring a green every time in the three consecutive plays of spinning wheel using the equation as shown below.
Exercises 1-26 involve probabilities with independent events.
Use the spinner shown to solve Exercises 1-10. It is equally probable that the pointer will land on any one of the six regions. If the pointer lands on a borderline, spin again. If the pointer is spun twice, find the probability it will land on
If the pointer is spun three times, find the probability it will land on
1.
2.
Show that the following are not logically equivalent by finding a counterexample:
(p^q) →r and
(db) V (d←d)
Show that the following is not a contradiction by finding a counterexample:
(pV-q) AqA (pv¬q Vr)
3.
Here is a purported proof that (pq) ^ (q → p) = F:
(db) v (bd) = (db) v (bd)
=(qVp) A (g→p)
= (¬¬q V ¬p) ^ (q→ p)
(db) V (db) =
=¬(a→p)^(a→p)
= (gp) ^¬(a → p)
=F
(a) Show that (pq) ^ (q→p) and F are not logically equivalent by finding a counterex-
ample.
(b) Identify the error(s) in this proof and justify why they are errors. Justify the other steps
with their corresponding laws of propositional logic.
Question 2: When John started his first job, his first end-of-year salary was $82,500. In the following years, he received salary raises as shown in the following table.
Fill the Table: Fill the following table showing his end-of-year salary for each year. I have already provided the end-of-year salaries for the first three years. Calculate the end-of-year salaries for the remaining years using Excel. (If you Excel answer for the top 3 cells is not the same as the one in the following table, your formula / approach is incorrect) (2 points)
Geometric Mean of Salary Raises: Calculate the geometric mean of the salary raises using the percentage figures provided in the second column named “% Raise”. (The geometric mean for this calculation should be nearly identical to the arithmetic mean. If your answer deviates significantly from the mean, it's likely incorrect. 2 points)
Hint for the first part of question 2: To assist you with filling out the table in the first part of the question,…
Chapter 11 Solutions
Thinking Mathematically, Books a la Carte Edition plus MyLab Math with Pearson eText -- Access Card Package, 4/e (7th Edition)
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Discrete Distributions: Binomial, Poisson and Hypergeometric | Statistics for Data Science; Author: Dr. Bharatendra Rai;https://www.youtube.com/watch?v=lHhyy4JMigg;License: Standard Youtube License