A survey of engineering firms reveals that 85% have their own mainframe computer (M), 16% anticipate...
Fantastic news! We've Found the answer you've been seeking!
Question:
Transcribed Image Text:
A survey of engineering firms reveals that 85% have their own mainframe computer (M), 16% anticipate purchasing a mainframe computer in the near future (B), and 5% have a mainframe computer and anticipate buying another in the near future. Find the probability that a randomly selected firm: (a) has a mainframe computer or anticipates purchasing one in the near future (4 marks) (b) does not have a mainframe computer and does not anticipate purchasing one in the near future (Hint: consider the Venn diagram of the event) (7 marks) 2 (c) has a mainframe computer given that it anticipates purchasing one in the near future (7 marks) (d) anticipates purchasing a mainframe computer given that it does not currently have one (7 marks) 3. (30 marks) "Go" is one of the oldest games in the world. The objective is to control territory by placing pieces called "stones" on vacant points on the board. Players alternate placing their stones. The player using black stones goes first, followed by the player using white stones. The following table shows the result of a study about the advantage of playing first (i.e., using the black stones) in Go. Number of Wins Number of Games Black Player Level Opponent Level T T 64 116 T L 33 34 L T 8 40 L L 15 30 Total: 120 220 In this table, "T" represents the top-level players and "L" represents the low-level players. When a game randomly selected from this study, let W be the event that the black player wins and TT, TL, LT, and LL be the events of different levels of players combinations. (a) Estimate the probability of winning when one plays first if we randomly select a game in the study. (3 marks) (b) Estimate the probability of winning when one plays first for each combination of the levels of players. (4 marks) (c) If we randomly select a game in the study and it is known that the players are at the same level, what is the probability that the black player wins? (3 marks) (d) Suppose there are five players. Two of them are top-level players and three of them are low-level players. Two players are randomly selected to play Go. One of these two players is randomly selected to be the black player. i. What is the probability that the black player wins? (6 marks) ii. Given that the players are at the same level, what is the probability that the black player wins? (Hint: Let A, B and C be events. It is known that An (BUC)=(ANB) U(ANC)) (8 marks) iii. Suppose it is known that black player wins. What is the probability that the black player is ranked lower than the white player? (6 marks) 4. (20 marks) Two years ago, a statistician estimated that the probability of the exis- tence of Superman is 0.18 based on the evidences in the physical world. He wants to improve his estimation by considering the evidences in morality. He estimates that if Superman exists, the probability that Superman prevents evil (that is, evil does not exist) is 0.78. If Superman does not exist, the probability that the evil exists is 0.5. Given the fact that evil exists, what is the revised probability of the existence of Superman? ~ End~ A survey of engineering firms reveals that 85% have their own mainframe computer (M), 16% anticipate purchasing a mainframe computer in the near future (B), and 5% have a mainframe computer and anticipate buying another in the near future. Find the probability that a randomly selected firm: (a) has a mainframe computer or anticipates purchasing one in the near future (4 marks) (b) does not have a mainframe computer and does not anticipate purchasing one in the near future (Hint: consider the Venn diagram of the event) (7 marks) 2 (c) has a mainframe computer given that it anticipates purchasing one in the near future (7 marks) (d) anticipates purchasing a mainframe computer given that it does not currently have one (7 marks) 3. (30 marks) "Go" is one of the oldest games in the world. The objective is to control territory by placing pieces called "stones" on vacant points on the board. Players alternate placing their stones. The player using black stones goes first, followed by the player using white stones. The following table shows the result of a study about the advantage of playing first (i.e., using the black stones) in Go. Number of Wins Number of Games Black Player Level Opponent Level T T 64 116 T L 33 34 L T 8 40 L L 15 30 Total: 120 220 In this table, "T" represents the top-level players and "L" represents the low-level players. When a game randomly selected from this study, let W be the event that the black player wins and TT, TL, LT, and LL be the events of different levels of players combinations. (a) Estimate the probability of winning when one plays first if we randomly select a game in the study. (3 marks) (b) Estimate the probability of winning when one plays first for each combination of the levels of players. (4 marks) (c) If we randomly select a game in the study and it is known that the players are at the same level, what is the probability that the black player wins? (3 marks) (d) Suppose there are five players. Two of them are top-level players and three of them are low-level players. Two players are randomly selected to play Go. One of these two players is randomly selected to be the black player. i. What is the probability that the black player wins? (6 marks) ii. Given that the players are at the same level, what is the probability that the black player wins? (Hint: Let A, B and C be events. It is known that An (BUC)=(ANB) U(ANC)) (8 marks) iii. Suppose it is known that black player wins. What is the probability that the black player is ranked lower than the white player? (6 marks) 4. (20 marks) Two years ago, a statistician estimated that the probability of the exis- tence of Superman is 0.18 based on the evidences in the physical world. He wants to improve his estimation by considering the evidences in morality. He estimates that if Superman exists, the probability that Superman prevents evil (that is, evil does not exist) is 0.78. If Superman does not exist, the probability that the evil exists is 0.5. Given the fact that evil exists, what is the revised probability of the existence of Superman? ~ End~
Expert Answer:
Related Book For
Management Science The Art of Modeling with Spreadsheets
ISBN: 978-1118582695
4th edition
Authors: Stephen G. Powell, Kenneth R. Baker
Posted Date:
Students also viewed these mathematics questions
-
Since Ryanair DAC's2 emergence as an upstart challenger to the Aer Lingus Ltd.-British Airways plc duopoly in the late 1980s, it had been both a consumer champion and antagonist; a technological...
-
CANMNMM January of this year. (a) Each item will be held in a record. Describe all the data structures that must refer to these records to implement the required functionality. Describe all the...
-
Solve Prob. 410 using singularity functions. Use statics to determine the reactions. Prob. 410, The figure shows a cantilever consisting of steel angles size 100 Ã 100 Ã 12 mm mounted...
-
Excel can be used to generate random integers between 0 and 9 inclusive. Suppose the following results are obtained. Use a 0.05 significance level to test the claim that the computer generates digits...
-
In Exercises determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The zeros of coincide with the zeros of P(x). f(x) = p(x) q(x)
-
Consider a $2^{3}$ experiment with factors A, B, and C. Show that \[\begin{aligned}I N T(A, B, C) & =\frac{1}{2}[I N T(A, C \mid B+)-I N T(A, C \mid B-)] \\& =\frac{1}{2}[I N T(C, B \mid A+)-I N T(C,...
-
New Business Ventures, Inc., has an outstanding perpetual bond with a 9 percent coupon rate that can be called in one year. The bond makes annual coupon payments and has a par value of $1,000. The...
-
How should the total consideration given to acquire control through a share purchase be allocated prior to preparing consolidated financial statements?
-
Jaxson, Inc., a calendar year S corporation, is partly owned by Jean Michele, whose beginning stock basis is $125,000. During the year, Jean Michele's share of a Jaxon long-term capital gain (LTCG)...
-
Consider a job where you are currently employed, or a prior job. A) Perform a job analysis on that job. What tasks are required? What knowledge, skills, and abilities are necessary to perform those...
-
Name differences in accounting and financial reporting for the federal government by examining the government - wide annual report.
-
Company Gold closes its accounts on a yearly basis, that is on December 31 of each year. On 1/4/2020, the company purchased an insurance policy for 3 years and paid the full amount of $ 25,200 in...
-
Remember arithmetic and symbolic languages used to do symbolic thinking. Are you more of a verbal, visual or symbolic thinker? Explain your answer. Discuss the role symbolic thinking has played in...
-
Social Media Marketing for Expansion A guest speaker at a small business development conference has a main audience of business owners who want to incorporate social media marketing into their...
-
Motivation is a complex subject, but its understanding and application is central to the success of management and the organization. Imagine that the CEO of your organization has tasked you with...
-
Describe a job you have had in the past or a job you are very familiar with. Indicate the negative aspects of the job and how it could be improved with current human resource management techniques.
-
The first three energy levels \(E(\mathrm{eV})\) of the fictitious element \(\mathrm{X}\) are \(\ldots . . \ldots\) shown in Figure P29.56. a. What wavelengths are observed in the absorption spectrum...
-
A sodium atom in the \(3 p\) state emits a photon, decreasing the energy of the atom by \(2.10 \mathrm{eV}\). By how much does the orbital angular momentum of the atom change? Does it increase or...
-
Assume instead that the spot exchange rate between the dollar and Swiss franc is a fixed or pegged rate within a narrow band around a central rate. For each change shown in Problem 9, assume that...
Study smarter with the SolutionInn App