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An analyst estimates there is a probability of 20 percent that there will be a recession next year. He thinks the probability of things being normal is three times the probability of a recession, with the remaining probability assigned to a boom taking place. A stock is expected to return -17 percent in a recession, 13 percent under normal conditions and 21 percent if there is a boom. What is the expected return (in percent) on this stock? Answer to two decimals, carry intermediate calcs. to four decimals.

There are many definitions of probability. The main one is that it is a measure of the likelihood of occurrence of events and has a value between 0 and 1. The closer the value is to 1, the more likely the event is....So, an event with probability 0 that mean it will never occur.

In a random experiment, the set of all possible outcomes are defined as the sample space and sometimes can be listed and sometimes can't. Sometimes our interest is limited to certain outcomes that make a certain event. For example, if you roll 2 dice, there are 36 possible outcomes in total. But, you may be interested in the event of getting a sum of 10, rather than all 36 possible outcomes that make up the sample space. In this case, if you denote the event by A, then A= the event of getting a sum of 10 consists of three outcome, in particular A = { (4,6), (5,5), (6,4)}. Assuming that the dice are fair (not biased), then P(A) = The probability of the event A =#(A)/#(S) = 3/ 36 and so on. If you let the event B be at least one of the dice is 4,in this case   B ={ (1,4), (2,4), (3,4),(4,4), (5,4) ,(6,4), (4,1),(4,2), (4, 3),(4,5), (4,6)},

P(B)= 11/36, P(A and B) = 2/36, and P(A union B) =12/36. So, Find P(A given B)= P(A|B) = P(A and B)/ P(B) =(2/36)/ (11/36) =2/11, which is more than twice P(A). Right?

Obviously, A and B are not mutually exclusive but Are they independent? (Hint: Just look at the example and the definition of independence)

In general, if you have 2 events A and B, what does it mean for these 2 events to be independent? How about mutually exclusive? Can they be both? Explain.

What is probability sample? discuss and give example

In a family with 7 children, excluding multiple births, what is the probability of having exactly 2 girls?
Assume that having a boy is as likely as having a girl at each birth.

A coin is tossed 8 times.

a) How many different outcomes are possible?

b) What is the probability of getting exactly 2 heads?

c) What is the probability of getting at least 2 heads?

d) What is the probability of getting at most 4 heads?

In the United States, voters who are neither Democrat nor Republican are called Independent. It is believed that 13% of voters are Independent. A survey asked 26 people to identify themselves as Democrat, Republican, or Independent.

A. What is the probability that none of the people are Independent?

Probability =

B. What is the probability that fewer than 5 are Independent?

Probability =

C. What is the probability that more than 2 people are Independent?

Probability =

The probabilities below reveal the intergenerational income movement. Mother= Bottom Third, Daughter = Bottom Third, Probability = 0.6; Mother= Bottom Third, Daughter = Middle Third, Probability = 0.25; Mother= Bottom Third, Daughter = Top Third, Probability = 0.15; Mother= Middle Third, Daughter = Bottom Third, Probability = 0.25; Mother= Middle Third, Daughter = Middle Third, Probability = 0.5; Mother= Middle Third, Daughter = Top Third, Probability = 0.25;Mother= Top Third, Daughter = Bottom Third, Probability = 0.15; Mother= Top Third, Daughter = Middle Third, Probability = 0.25; Mother= Top Third, Daughter = Top Third, Probability = 0.6. Find the probability that the granddaughter (along the maternal line) of a woman in a top third of the income distribution will remain in this group.

a. .80

b. .60

c. .45

d. .25

Whether liberating or alienating, we are still interdependent, and in a world of strangers it is they on whom we must rely. I trust the skill of people around the world when I buy my clothes, drive my car, and eat my food. I trust engineers, contractors, and inspectors when I cross a bridge, ride an elevator, or fly in an airplane. I trust I will receive fair treatment by such strangers as librarians, ambulance drivers, nurses or doctors, policemen or firemen.

They are there to serve strangers. Our territorial segmentation makes us strangers and our global integration makes us depend on and trust strangers often more than family and friends. We know we are linked globally because we have constructed communication and transportation links to tie us all together.

These networks empower us-our actions go far beyond the local to transform nature and culture virtually anywhere. The networks are so complex and shifting that we are rarely able to trace the extent and consequences of our actions.

What is Robert Sack saying?

Even though you live in Spain, how are you personally connected to the mining of minerals on the continent of Africa?

DaisyRose, Inc is an accounting firm with 30 accountants and has about $3 million annually in net revenues. They are located in an older office building that has a standard elevator. The accountant job descriptions require that they be able to analyze and prepare financial statements and tax returns for clients.

One of the accountants on staff, Iris, has developed macular degeneration and   because of that cannot see a standard computer screen. His doctors have told him that in the next few months he will not be able to see any computer screen. Iris has learned braille (raised type that allow those without sight to read). Iris approaches the CEO of DaisyRose to indicate that he needs voice activated software for his computer and that he would also need the computer to print in Braille so that he could read the returns and statements. Iris has also asked that the elevators be equipped with Braille on the touchpad so that he knows the proper buttons for each floor. The CEO calculates that all of these requests will cost about $100,000 up front and about $20,000 per year after that initial investment.

Please evaluate these facts under the Americans with Disabilities Act to determine whether or not the company will need to make the requested changes.

Question

You are within two weeks of turnover of a three-story build-to-suit office building project. Many of the city inspections are complete and it appears that a certificate of occupancy (C of O) will be obtained on time. Only the fire protection, elevator, and life safety inspections remain. The mechanical, electrical, fire protection and life safety were all design-build systems. During the punch list, it is discovered that the fire protection subcontractor has installed a different type of sprinkler head on each floor. The first floor uses concealed heads with white escutcheons to match the ceiling tiles. The second floor uses decorative chrome heads. The subcontractor installed semi-recessed heads on the third floor. This was not picked up prior as a person cannot physically see more than one floor at a time. The client is very upset. Questions: 1. Can you require the subcontractor to change them all out now? 2. Would this be a good move given the status of the inspections? 3. Who is responsible to check and approve the shop drawings and submittals for design-build subcontractors? 4. What should the general Contractor have done to prevent this from happening? 5. What can you do now?

THE BOLDED LETTER AND NUMBER IS THE GIVEN ANSWER. ONE OF THE BOLDED ANSWERS ARE INCORRECT, WHICH ONE IS INCORRECT AND WHAT IS THE CORRECT ANSWER?

Your company manufactures hot water heaters. The life spans of your product are known to be normally distributed with a mean of 13 years and a standard deviation of 1.5 years. You want to set the warranty on your product so that you do not have to replace more than 5% of the hot water heaters that you sell. How many years should you claim on your warranty?

In a highway construction zone with a posted speed limit of 40 miles per hour, the speeds of all vehicles are normally distributed with a mean of 46 mph and a standard deviation of 3 mph. Find the probability that the speed of a random car traveling through this construction zone is more than 45 mph.

The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 6.7 minutes and a standard deviation of 2.1 minutes. Find the probability that the delivery time for a random order at this restaurant is between 7 and 8 minutes.

The average number of pounds of red meat a person consumes each year is 196 with a standard deviation of 22 pounds (Source: American Dietetic Association). This distribution is approximately bell-shaped and symmetric. If an individual is randomly selected, find the probability that the number of pounds of red meat they consume each year will be less than 200 pounds.

The pucks used by the National Hockey League for ice hockey must weigh between 5.5 and 6.0 ounces. Suppose the weights of pucks produced at a factory are normally distributed with a mean of 5.75 ounces and a standard deviation of 0.11 ounces. What percentage of pucks produced at this factory cannot be used by the National Hockey League?

1. The distribution of scores on a statistics final exam is approximately normal with a mean of 62 and a standard deviation 11. Find the z-score for a score of 77 on the statistics final exam.