If the probability is 0.70 that any one person interviewed at a shopping mall will be against an increase in the sales tax to finance a new football stadium,

(a) What is the probability that among four persons interviewed at the mall the first three will be against the increase in the sales tax, but the fourth will not be against it?

(b) What is the probability that among four persons interviewed at the mall three will be against the increase in the sales tax?

(c) What is the probability that among ten persons interviewed at the mall seven will be against the increase in the sales tax?

(d) What is the probability that the fourth person interviewed is the first to be against the increase in the sales tax?

(e) What is the probability that seven persons will be interviewed before ending four who will be against the increase in the sales tax?

You are considering investing in a project in Australia. There are several risks that you think have the potential to significantly affect project performance. The risks you are concerned about are as follows: * AUD currency value. You think the probability of depreciation is 0.24, the probability of stable value is 0.54, and the rest is the probability of appreciation. * General economic conditions. Probability of weak economy is 0.18, average economy 0.11, and the rest is good economy. * Local tax rates. Probability of increased tax rate is 0.27, and the rest is stable tax rate. There are 18 possible states of the world you will be working with. Assume all these events are independent. What is the probability of stable currency value, good economy, and increased tax rate? Enter answer in percents.

The probability that house sales will increase in the next 6 months is estimated to be 0.25. The probability that the interest rates on housing loans will go up in the same period is estimated to be 0.74. The probability that house sales or interest rates will go up during the next 6 months is estimated to be 0.89. 1) The probability that house sales will increase but interest rates will not is 2) The events increase in house sales and increase in interest rates in the next 6 months are a) independent. b) mutually exclusive. c) have a probability =1. d) None of the above. 3. The events increase in house sales and no increase in house sales are a) independent. b) mutually exclusive. c) have a probability =1. d) (b) and (c)

Part I (investigating patterns)

         Assume that you are trying to achieve a certain goal and the probability of your success P(S) is only 20% and that your capabilities are not increasing over time, that is your probability of success is constant.

         1.       Show that the probability of unsuccessful attempt P(U) is 0.8.

          Given that you did not succeed the first time, find the probability that you succeed the second time.

          Given that you did not succeed in the first two attempts, find the probability that you succeed the third time.

          Given that you did not succeed in the first (n – 1) attempts, find the probability that you succeed in the nth attempt.

          What is the relation between the events S and U that lead to the results above?

2) I am about to choose an integer, at random, from amongst the following positive integers: {1,2,3,4, …., 25, 26, 27}

a) is this an example of discrete or continuous uniform probability distribution? Please explain

b) what is the probability that I coincidentally happen to choose integer “23”? show work

c) please depict this probability distribution in some appropriate manner.

d) please determine the probability that I choose: either an even integer, or an integer which is at least 20? Recall: PROB(A or B)+PROB(B)-PROB(A&B). show work

e) please determine the mean value for this probability function. Show work

f) please determine the standard deviation for this probability function. Show work

Assume there is a medical test to diagnose a disease. If a person has the disease, the probability of having positive test result is 98 percent. If a person does not have the disease, the probability of having negative test results is 99.6 percent. The probability that a person has a disease is 1 percent in the population.

Answer the following questions:

a) If a person has a positive test result, what is the probability that he/she has the disease?

b) If a person has a positive test result, what is the probability that s/he doesn’t have the disease?

c) If a person has a negative test result, what is the probability that he/she doesn’t have the disease?

d) If a person has a negative test result, what is the probability that s/he has the disease?

Note: Use the following notation in your answer:

D: Person with disease

ND: Person without disease

+T: Positive test result

- T: Negative test result

Write each question in the form of mathematical notation for conditional probability.

Calculate the answer using two methods:

1. Bayes’ rule and conditional probability equations.

2. Draw a table, assume a population (e.g. 1 million) and provide numerical answers

Question 1

Which of the following is true about disability insurance?

Select one:

a. Because the chance of becoming disabled is small, most people do not purchase disability insurance coverage.

b. The probability of a 35 year becoming disabled for three months or longer before age 65 is 20 percent.

c. Older people are less likely to become disabled than younger people.

d. For people who become disabled longer than three months, the average length of time is 2.9 years.

Question 2

Property damage liability covers damages to your car from accidents that are your fault.

Select one:

True

False

Question 3

The Canada Pension Plan is the easiest disability coverage to qualify for benefits.

Select one:

True

False

Question 4

For auto insurance, which area has the highest level of insurance coverage required by law?

Select one:

a. Third party liability coverage

b. Uninsured motorist coverage

c. Comprehensive coverage

d. Accident benefits coverage

Question 5

Which of the following is true regarding employer sponsored long term disability insurance?

Select one:

a. The most important issue to consider is the definition of disability used.

b. Disability benefits are provided for very long periods, usually to full retirement.

c. All large and medium-sized firms offer an optional disability plan through an insurance company.

d. A typical disability policy covers about 90 percent of the employee's salary.

The Chamber of Commerce in a Canadian city has conducted an evaluation of 300 restaurants in its metropolitan area. Each restaurant received a rating on a 3-point scale on typical meal price (1 least expensive to 3 most expensive) and quality (1 lowest quality to 3 greatest quality). A crosstabulation of the rating data is shown below. Forty-five of the restaurants received a rating of 1 on quality and 1 on meal price, 42 of the restaurants received a rating of 1 on quality and 2 on meal price, and so on. Thirty of the restaurants received the highest rating of 3 on both quality and meal price.

(a)

Develop a bivariate probability distribution for quality and meal price of a randomly selected restaurant in this Canadian city. Let

x = quality rating

and

y = meal price.

(b)

Compute the expected value and variance for quality rating, x.

(c)

Compute the expected value and variance for meal price, y.

(d)

The

Var(x + y) = 1.51.

Compute the covariance of x and y. What can you say about the relationship between quality and meal price? Is this what you would expect?

(e)

Compute the correlation coefficient between quality and meal price. What is the strength of the relationship? Do you suppose it is likely to find a low-cost restaurant in this city that is also high quality? Why or why not?

A 10-year study conducted by the American Heart Association provided data on how age, blood pressure, and smoking relate to the risk of strokes. Data from a portion of this study follow. Risk is interpreted as the probability (times 100) that a person will have a stroke over the next 10-year period. For the smoker variable, 1 indicates a smoker and 0 indicates a nonsmoker.

b. Using the best regression procedure, how many independent variables are in the highest adjusted R ² model?

What is the value of R ²(adj)? Note: report R ²(adj) as a percentage (to 1 decimal).

Show the best regression model below (to 3 decimals, if necessary). Enter 0 if the independent variable listed below is not in your best regression model.

Rating = ______ + ________ Age + ________ Pressure + ________Smoker

One of Philip’s investments is going to mature, and he wants to determine how to invest the proceeds of $50,000. Philip is considering two new investments: a stock mutual fund and a one-year certificate of deposit (CD). The CD is guaranteed to pay a 3% return. Philip estimates the return on the stock mutual fund as 11%, 2%, or -9%, depending on whether market conditions are good, average, or poor, respectively. Philip estimates the probability of a good, average, and poor market to be 35%, 40%, and 25%, respectively.

(Question 1) Construct a payoff table (in dollars) for this problem.

(Question 2) What decision should be made according to the optimistic approach?

(Question 3) Create a regret table for Philip. What decision should be made according to the minimax approach?

(Question 4) What decision should be made according to the expected value approach?

(Question 5) How much should Philip be willing to pay to obtain a market forecast that is 100% accurate?

ANSWERS I'VE CALCULATE ALREADY

1.)

2. The optimistic approach involves selecting the alternative that maximizes the maximum payoff available. Therefore, the highest payoff is under stock when the market is in good condition.