1. Write a C++ program to check whether a number is prime or not. A prime number is a positive integer that has exactly two positive integer factors, 1 and itself. Eg: 2, 3, 5, 7, 11, 13, 17, ...

   Sample Output:
   Input a number to check prime or not: 13 The entered number is a prime number.

   Input a number to check prime or not: 28 The entered number is not a prime number.

   Enhance the program to list all factors if the number is not prime Input a number to check prime or not: 28
   The entered number is not a prime number.
   Factors: 1, 2, 4, 7, 14, and 28

  Boardman Gases and Chemicals is a supplier of highly purified gases to semiconductor manufacturers. A large chip producer has asked Boardman to build a new gas production facility close to an existing semiconductor plant. Once the new gas plant is in​ place, Boardman will be the exclusive supplier for that semiconductor fabrication plant for the subsequent 10 years. Boardman is considering one of two plant designs. The first is ​ Boardman's "standard" plant which will cost 38.3 million to build. The second is for a​ "custom" plant which will cost $53.3 million to build. The custom plant will allow Boardman to produce the highly specialized gases required for an emergency semiconductor manufacturing process. Boardman estimates that its client will order ​$11.7 million of product per year if the standard plant is​ constructed, but if the custom design is put in​ place, Boardman expects to sell ​$17.1 million worth of product annually to its client. Boardman has enough money to build either type of​ plant, and, in the absence of risk​ differences, accepts the project with the highest NPV. The cost of capital is 16.6​%.

A. Find the NPV for each project. Are the projects​ acceptable?

B. Find the breakeven cash inflow for each project.

C. The firm has estimated the probabilities of achieving various ranges of cash inflows for the two projects, as shown in the table..... What is the probability that each project will achieve the breakeven cash inflow found in part B?

Probability of achieving cash inflows in given range

Range of cash inflows Standard plant Custom Plant

$0 to 5 0% 5%

5 to 8 10 10

8 to 11 60 15

11 to 14 25   25

14 to 17 5    20

17 to 20 0 15

above 20 0 10

d. Which project is more​ risky? Which project has the potentially higher​ NPV? Discuss the​ risk-return trade-offs of the two projects.

e. If the firm wished to minimize losses​ (that is, NPV less than $ 0NPV<$0​), which project would you​ recommend? Which would you recommend if the goal was achieving a higher​ NPV?

Boardman Gases and Chemicals is a supplier of highly purified gases to semiconductor manufacturers. A large chip producer has asked Boardman to build a new gas production facility close to an existing semiconductor plant. Once the new gas plant is in​ place, Boardman will be the exclusive supplier for that semiconductor fabrication plant for the subsequent 10 years. Boardman is considering one of two plant designs. The first is ​ Boardman's "standard" plant which will cost ​$39.1 million to build. The second is for a​ "custom" plant which will cost ​$54.1 million to build. The custom plant will allow Boardman to produce the highly specialized gases required for an emergency semiconductor manufacturing process. Boardman estimates that its client will order​$12.3 million of product per year if the standard plant is​ constructed, but if the custom design is put in​ place, Boardman expects to sell ​$16.7 million worth of product annually to its client. Boardman has enough money to build either type of​ plant, and, in the absence of risk​ differences, accepts the project with the highest NPV. The cost of capital is 17.2%.

a. Find the NPV for each project. Are the projects​ acceptable?

b. Find the breakeven cash inflow for each project.

c. The firm has estimated the probabilities of achieving various ranges of cash inflows for the two​ projects, as shown in the table. What is the probability that each project will achieve the breakeven cash inflow found in part ​(b​)​?

d. Which project is more​ risky? Which project has the potentially higher​ NPV? Discuss the​ risk-return trade-offs of the two projects.

e. If the firm wished to minimize losses​ (that is, NPV < $0​), which project would you​ recommend? Which would you recommend if the goal was achieving a higher​ NPV?

2.Deck of cards(52 total cards; 13 denominations in each of 4 suits). Select a single card at random from a deck of cards:

a.Whatis the probability of selecting the king of hearts?

b.What is the probability of selecting a king?

c.What is the probability of selecting a heart?

d.What is the probability of selecting a king or a heart?

3. Box A contains 6 red balls and 3 green balls, whereas box B contains 3 red ball and 15 green balls.

Stage one:One box is selected at random in such a way that box A is selected with probability 1/5 and box B is selected with probability 4/5.

Stage two: First, suppose that 1 ball is selected at random from the box selected at stage one.

a) What is the probability that the ball is red?

b) Given that the ball is red, what is the probability it came from box A? Next, suppose that two balls are selected at random without replacement from the box selected at stage one.

c) What is the probability that both balls are red?

d) Given that both balls are red, what is the probability they came from box A?

e) What is the probability that one ball is red and the other is green?

f) Given that one ball is red and the other is green, what is the probability they came from box A?

A recent survey conducted by a foundation reported that 74​% of teens admitted to texting while driving. A random sample of 42 teens is selected. Use the normal approximation to the binomial distribution to answer parts a through e.

a. Calculate the mean and standard deviation for this distribution.

The mean is _________.

​(Round to four decimal places as​ needed.)

The standard deviation is ___________.

b. What is the probability that more than 36 of the 42 teens admit to texting while​ driving?

The probability is __________..

​(Round to four decimal places as​ needed.)

c. What is the probability that exactly 24 of the 42 teens admit to texting while​ driving?

The probability is _____________.

​(Round to four decimal places as​ needed.)

d. What is the probability that 27​, 28​, or 29 of the 42 teens admit to texting while​ driving?

The probability is ___________.

​(Round to four decimal places as​ needed.)

e. What is the probability that fewer than 32 of the 42

teens admit to texting while​ driving?

The probability is ___________.

​(Round to four decimal places as​ needed.)

(i) Develop your written part by answering the six questions given in the case. Each question may be answered in about 150 to 200 words. (50% to the marks)

(ii) Develop a PowerPoint presentation. You have to take one side, either the company ThyssenKrupp or the fired employee. If you decide to represent ThyssenKrupp, then you are the defense lawyer. If you decide to represent the fired mechanic, you are the Plaintiff’s Lawyer. Present your arguments with evidence and supporting matter to the Judge (Raj Mohanty) via a PowerPoint presentation. In a courtroom, the Judge is always addressed as “Me Lord” or “Your Honor”. (50% to the marks) No presentation in the classroom or on Adobe Connect will be needed. Your only chance to convince the judge is through your PowerPoint

. ThyssenKrupp Elevator Canada INTRODUCTION During a lunchroom break, a male employee at ThyssenKrupp decided to take up a dare from a fellow colleague for $100 and the Jackass-like prank was videotaped then posted to YouTube. When it came to the attention of the HR manager and other senior management, the employee was fired for violating company policy. The employee argued in court that the organizational culture allowed such behavior. But would the Ontario Labour Relations Board (OLRB) agree?

BACKGROUND ThyssenKrupp Elevator Canada was subcontracting elevator installation at a construction site in downtown Toronto where a large office building was being built. All the workers on the site, including those from ThyssenKrupp, and the main contractor of the site, PCL Construction, were male and the culture of the workplace was described as a “macho” environment where pranks were played. There were reportedly pictures of women and provocative calendars hanging on walls, as well as signs displaying vulgar humor. There was little concern about these as access to the building was restricted to people involved in the construction project. One of ThyssenKrupp's employees at the site was an elevator mechanic. He and several other employees engaged in what he called “picking” on each other and playing pranks to keep things light at work. They also watched pornographic scenes on a worker's iPod and episodes of the television show Jackass, which features individuals doing stupid activities on dares.

ESCALATION OF PRANK BEHAVIOUR Over a period of a few weeks, the mechanic and other employees performed more and more pranks that copied some of the ones they saw on the Jackass show. Typically these events took place in the basement lunchroom where employees gathered for breaks and meals, to change clothes, and to socialize. Soon, money was being offered on dares to do certain actions. For example, one ThyssenKrupp employee accepted a dare that involved a $60 payment—money collected from fellow employees, including three foremen. The dare involved the employee eating spoiled food found in the common refrigerator of the lunchroom. A couple of weeks after the first dare, the mechanic was observed playing with a stapler in the lunchroom on a break. One of the foremen walked in and jokingly said, “What are you going to do with that? Why don't you staple your nuts to something?” The mechanic jokingly replied that he'd do it “if you get enough money.” Though he claimed it was intended as a joke, word spread within a few hours, and soon $100 was raised among seven other ThyssenKrupp and three PCL employees. Another four people were in the lunchroom later that afternoon watching when the mechanic decided to go ahead with the staple dare. He proceeded to drop his work uniform trousers and staple his scrotum to a wooden plank, which was met by “cheering and high fives,” according to the mechanic. With the mechanic's knowledge, the prank was filmed on video. Included on-camera were all those employees present, wearing full worksite uniforms, PCL logos on hats, and TK shirt patches—all easily identifiable and recorded by a worker who was present that day. The mechanic was advised at a later date that the event was posted on YouTube. Initially, the mechanic did nothing about the YouTube posting but eventually asked for it to be taken off the site. To ensure this was done, the mechanic went back to YouTube searching for the video clip, but couldn't find it. He assumed it had been removed, however, it was not—he just didn't search correctly. In total, the video clip was assessable on YouTube for two weeks, during which time many employees in the construction industry watched it. It was during these two weeks that ThyssenKrupp became aware of the video after the HR department received an email with a link to the video, and several people discussed it with a ThyssenKrupp executive at a construction labor relations conference. Conference participants insisted the employee was from ThyssenKrupp, and they questioned how the company could allow something like that to happen during work hours. At this point, ThyssenKrupp management reviewed the video one more time and decided that the mechanic had violated its workplace harassment policy, which prohibited “practical jokes of a sexual nature which cause awkwardness or embarrassment.” The mechanic was fired for “a flagrant violation” of ThyssenKrupp's harassment policy and risking the company's reputation.

CULTURE AT FAULT Upon being fired from his job, the mechanic filed a grievance with the OLRB. He argued that dismissal was too harsh given the culture of the workplace which was accepting of that type of behavior. He also said no one told him not to do it, no one expressed displeasure, and no one mentioned they were offended. He argued that other employees had done stunts but questioned why he was the only one disciplined for his actions. He also claimed to have never seen the workplace harassment policy, even though it was part of the orientation package. THE DECISION In July 2011, the OLRB found the mechanic's misconduct on the employer's premises, plus his permission to record it, “patently unacceptable in almost any workplace.” The fact that his employer was easily identified in the video clip contributed to the decision. The fact that the mechanic claimed not to have known about the corporate harassment policy was irrelevant—he should have known better. The OLRB also dismissed as irrelevant that no one protested or objected to the prank during the lunch break, which the mechanic argued was “not during work hours.” The court stated that ThyssenKrupp has an interest in preventing such horseplay and stunts in the workplace. They are in a safety-sensitive industry and such employee misconduct places the firm's reputation in jeopardy. The seriousness of the mechanic's misconduct also superseded any other factors, such as his claim of being a good employee with a clean record and the argument around the culture. There was no evidence that the company was aware of other pranks, and his role as the principal offender wasn't diminished by the culture, said the board. In dismissing the mechanic's grievance, the board stated, “If (ThyssenKrupp) employees want to emulate the principles of Jackass by self-abuse, they may be free to do so when they are not on the (employer's) premises and cannot be identified as being associated with (ThyssenKrupp).”

Questions

(1) What corporate values did ThyssenKrupp refer to when deciding to terminate the mechanic? What are the health and safety issues involved here? Do you think an informal work environment is leading towards a lack of strict health & safety policy at the workplace?

(2) Considering that the mechanic claimed that the ThyssenKrupp culture contributed to such behavior, in your opinion, does ThyssenKrupp need to change its corporate culture? If not, why not?

(3) Are there any Tort issues involved here? What other legal issues are involved here? Explain.

(4) Did the Ontario Labour Relation Board (OLRB) accept the defense that organizational culture contributed to the employee behavior? Explain their reasoning. Considering the company’s work environment, what factors need to be considered while updating the company’s health & safety policy?

(5) If this case goes to court, what arguments the Plaintiff’s Lawyer, representing the fired worker, would present before the court?

(6) What would be the line of Defense for the Lawyer of Thyssen Krupp Elevator?

1. New information obtained through research or experimentation that enables an updating or revision of the state-of-nature probabilities is known as

conditional probability.

joint probability.

sample information.

expected utility.

2.__________ refer to the probabilities of the states of nature after revising the prior probabilities based on sample information.

Preliminary probabilities

Joint probabilities

Posterior probabilities

Perfect probabilities

3._____ refers to the probability of one event, given the known outcome of a (possibly) related event.

Joint probability

Decisive probability

Conditional probability

A priori probability

4.Bayes’ theorem

enables the use of sample information to revise prior probabilities.

is useful for determining optimal decisions without requiring knowledge of probabilities of the states of nature.

can be used only for cases where conditional probabilities are unknown.

cannot be used to calculate posterior probabilities.

Highway engineers estimate that the main highway between two cities has a 1%

probability of being blocked in good weather, and a 5% probability of being blocked in

snowy weather. The detour route, on the other hand, is a smaller road which has a 2%

probability of being blocked in good weather and a 15% probability of being blocked when it

snows. On a certain day, forecasters predict a 60% chance of snow.

a.

Are the events that it snows and that the main highway is blocked

dependent or independent?

b.

Are the events that the highway is blocked and that the detour is blocked

dependent or independent?

c.

Find the overall probability that, on this day, the highway will be

blocked (whether or not the detour is blocked).

d.

Find the overall probability that, on this day, both the highway

and

the detour will be blocked.

e.

Find the probability that, on this day, either the highway, the detour, or both

will not be blocked.