Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 9, 8, and 7 for successfully completing the task in the allotted time Assuming that the teams work independently, what is the probability that the task will not be completed in time?

Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 9, 8, and 7 for successfully completing the task in the allotted time Assuming that the teams work independently, what is the probability that the task will not be completed in time?

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter11: Simulation Models

Section: Chapter Questions

Problem 45P: You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that...

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The game of Chuck-a-Luck is played as follows: You pick a number between 1 and 6 and toss three dice. If your number does not appear, you lose 1. If your number appears x times, you win x. On the average, use simulation to find the average amount of money you will win or lose on each play of the game.
It costs a pharmaceutical company 75,000 to produce a 1000-pound batch of a drug. The average yield from a batch is unknown but the best case is 90% yield (that is, 900 pounds of good drug will be produced), the most likely case is 85% yield, and the worst case is 70% yield. The annual demand for the drug is unknown, with the best case being 20,000 pounds, the most likely case 17,500 pounds, and the worst case 10,000 pounds. The drug sells for 125 per pound and leftover amounts of the drug can be sold for 30 per pound. To maximize annual expected profit, how many batches of the drug should the company produce? You can assume that it will produce the batches only once, before demand for the drug is known.
You have 5 and your opponent has 10. You flip a fair coin and if heads comes up, your opponent pays you 1. If tails comes up, you pay your opponent 1. The game is finished when one player has all the money or after 100 tosses, whichever comes first. Use simulation to estimate the probability that you end up with all the money and the probability that neither of you goes broke in 100 tosses.
You now have 10,000, all of which is invested in a sports team. Each year there is a 60% chance that the value of the team will increase by 60% and a 40% chance that the value of the team will decrease by 60%. Estimate the mean and median value of your investment after 50 years. Explain the large difference between the estimated mean and median.
You now have 5000. You will toss a fair coin four times. Before each toss you can bet any amount of your money (including none) on the outcome of the toss. If heads comes up, you win the amount you bet. If tails comes up, you lose the amount you bet. Your goal is to reach 15,000. It turns out that you can maximize your chance of reaching 15,000 by betting either the money you have on hand or 15,000 minus the money you have on hand, whichever is smaller. Use simulation to estimate the probability that you will reach your goal with this betting strategy.
A software company recently designed and developed a new service for its customers. However, it needs to decide whether to launch the service next month or wait for six months. The company performs research and discovers the probability of success for both options, along with their potential revenue. It also learns the probability of failure and corresponding losses for each. *Option A: Launching the service next month has a 55% probability of success with potential revenue of $250,000. It has a 45% probability of failure with a potential loss of $125,000.* *Option B: Launching the service in six months has a 65% probability of success with potential revenue of $400,000. It has a 35% probability of failure with a potential loss of $200,000.* Which option should the company pursue?
Hoping to increase the chances of reaching a performance goal, the director of a research project has assigned three separate research teams the same task. The director estimates that the team probabilities are 0.9, 0.8, and 0.7 for successfully completing the task in the allotted time. Assuming that the teams work independently, what is the probability that the task will not be completed in time? Round your answer to three decimal places.
At DataTech Solutions, the reliability of their server systems is a critical factor in maintaining smooth operations. The company knows that the probability of a server experiencing no downtime due to technical issues is 0.95. When a server is functioning smoothly, there is a 0.9 probability that the network performance is also optimal. However, if a server encounters technical problems, the probability of having optimal network performance drops to 0.3. A server is chosen at random for assessment, and its network performance is found to be optimal. What is the updated probability that the server is running without any technical issues?
A product is composed of four parts. In order for the product to function properly in a given situation, each of the parts must function. Two of the parts have a .96 probability of functioning, and twohave a probability of .99. What is the overall probability that the product will function properly?
A family of mutual funds maintains a service that allows clients to switch money among accounts through a telephone call. It was estimated that 3.2% of callers either get a busy signal or are kept on hold so long that they may hang up. Fund management assesses any failure of this sort as a $10 goodwill loss. Suppose that 2,000 calls are attempted over a particular period. a. Find the mean and standard deviation of the number of callers who will either get a busy signal or may hang up after being kept on hold. b. Find the mean and standard deviation of the total goodwill loss to the mutual fund company from these 2,000 calls.
A swim club is designing a new pool to replace its old pool. The new pool would need to last for 10 years since the club is planning on relocating after 10 years. A concrete shell would cost $85,000 and last for all 10 years. Another option is to install a vinyl liner that would cost only $70,000 to install. However, the vinyl is not guaranteed to last for all 10 years, and it has a 40% chance of breaking down. Repair of the vinyl would cost $40,000 and would extend the life of the vinyl liner to the 10-year mark. If both options are acceptable to the swim club, which one minimizes cost? Support your answer with drawing a decision tree and provide your calculation.
Discuss how likely it is that 70% of students will pass a college course with a B or an A. Then, consider the following questions: Would you look at data showing the success rate of previous courses? Would you check whether the current GPA of students in your class is high or low? What other data would you like to have before you determine the probability of 70% of students passing this course with a B or an A?