## Description

2.

A project manager estimates that there is 0.3 probability that the time to complete a project will exceed the deadline. Subsequently he receives a forecast from a project planning tool. This suggests that the deadline will be exceeded. In the past the tool has given this forecast on 90% of occasions when the deadline has been exceeded and on 20% of occasions when it has not. The posterior probability of the deadline being exceeded is (to two decimal places):

A) 0.30

B) 0.66

C) 0.27

D) 0.41

3.

Based on a quick examination, a computer specialist estimates that there is a 0.8 probability that a computer failure has been caused by a fault in the computer’s motherboard. However an electronic test, which has a 90% probability of giving a correct indication, and which can be assumed to be unbiased, indicates that the problem is not caused by the motherboard. The posterior probability that there is a fault in the motherboard is (to two decimal places):

A) 0.31

B) 0.08

C) 0.26

D) Impossible to calculate based on the information given

4.

An economist says that there is “absolutely no chance” of a country’s economy being in a recession in the last quarter of the year. However, a leading economic indicator which has a 70% probability of giving a correct indication, suggests that there will be a recession in this quarter. Given that the indicator is unbiased, the posterior probability of a recession in the last quarter of the year is:

A) 0

B) 0.7

C) 1

D) Impossible to calculate based on the information given

5.

An election forecasting model has a 50:50 chance of correctly predicting the election winner when there are two candidates. Before seeing the prediction of the model an election researcher estimates that there is a 75% chance that candidate Allan will defeat candidate Barnes. She then finds out that the model has predicted a victory for Barnes. Her posterior probability of a victory for Allan should be:

A) 0.375

B) 0.500

C) 0.750

D) 1.000

6.

A market research study will indicate that the sales of a new product in its first year will either be high, medium or low. Under which of these conditions would Bayes’ theorem indicate that the prior probabilities of high, medium and low sales should be revised when the new information from the study is received?

A) When the prior probability of high sales is equal to 1.0

B) When the study has the same probability of giving the three indications irrespective of the actual level of sales that will prevail

C) When the prior probabilities for all three events are the same and the research has a 60% chance of giving a correct indication

D) Under none of these conditions

7.

The prior probabilities that it will be fine or raining at 12:00 noon next Sunday when a parade is due to take place are respectively, 0.7 and 0.3. Two days before the event the local weather station will forecast either fine weather or rain for 12:00 noon on Sunday. Given that its forecasts are unbiased and have a 90% probability of being correct, the probability that it will forecast fine weather:

A) Cannot be determined based on the information given

B) Is equal to 0.70

C) Is equal to 0.66

D) Is equal to 0.63

8.

A food manufacturer has to decide how many batches of a product to produce next week. If one batch is produced then a profit of $15,000 will be made. If two batches are produced then either a loss of $5,000 will be made if demand only equals one batch or a profit of $20,000 will be made if demand equals two batches. The manufacturer provisionally estimates the probabilities of these two outcomes to be 0.4 and 0.6, respectively. After making these estimates the manufacturer finds that a statistical demand forecasting method suggests that demand will equal two batches. In the past the method has correctly predicted demand in 60% of weeks, irrespective of what the level of demand turned out to be. To maximize his expected profit the manufacturer should:

A) Produce 1 batch

B) Produce 2 batches

C) Be indifferent between producing 1 or 2 batches

D) Seek further information as it is not possible to compute the expected profits from this information

9.

With reference to the decision described in Question 8, suppose that the manufacturer had to decide whether it was worth paying for the forecast of the statistical demand forecasting method before making his decision. The expected value of imperfect information obtained from the method would have been:

A) $0

B) $2,700

C) $5,000

D) $7,800

10.

With reference to the decision described in Question 8, suppose that the statistical demand forecast always gave a correct indication. The expected value of perfect information obtained from the method would have been:

A) $0

B) $3,000

C) $6,000

D) $18,000

13.

Using the decision tree below:

(see chart on page 669-18-21, question #13)

What are the posterior probabilities of the high sales and low sales?

A) p(high sales) = 0.5625; p(low sales) = 0.4375

B) p(high sales) = 0.2470; p(low sales) = 0.7530

C) p(high sales) = 0.4375; p(low sales) = 0.5625

D) p(high sales) = 0.7530; p(low sales) = 0.2470

14.

Using the decision tree below:

(see chart on page 669-18-22, question #14)

What is the posterior probability that sales will be over $1 million?

A) 0.4615

B) 0.5385

C) 0.6872

D) 0.3128

16.

The managers of Red Valley Auto Products are considering a national launch of a new car cleaning product. For simplicity, the potential average sales of the product during its lifetime are classified as being either high, medium or low, and the NPV of the product under each of these conditions is estimated to be $80 million, $15 million and -$40 million respectively. The company’s marketing manager estimates that there is a 0.3 probability that average sales will be high, a 0.4 probability that average sales will be medium, and a 0.31 probability that sales will be low. It can be assumed that the company’s objective is to maximize expected NPV. Based on the decision tree below, determine whether the product should be launched.(see chart on page 669-18-23, question #16)

A) Yes, the product should be launched

B) No, the product should not be launched

17.

Based on the information in Question 16, what is the expected value of perfect information?

A) $30 million

B) Not enough information is provided to determine the EVPI

C) $18 million

D) $12 million

20.

At the extreme, if your prior probability of an event occurring is zero, then the posterior probability will be:

A) 0

B) 1

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## Explanation & Answer

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2. A project manager estimates that there is 0.3 probability that the time to complete a project will

exceed the deadline. Subsequently he receives a forecast from a project planning tool. This

suggests that the deadline will be exceeded. In the past the tool has given this forecast on 90% of

occasions when the deadline has been exceeded and on 20% of occasions when it has not. The

posterior probability of the deadline being exceeded is (to two decimal places):

A) 0.30

B) 0.66

C) 0.27

D) 0.41

ANSWER: B) 0.66

Solution

Project exceeds deadline

Project does not exceed deadline

Prior Conditional

0.30

0.90

0.70

0.20

Joint

0.30*0.90 = 0.27

0.70 * 0.20 = 0.14

0.27 + 0.14 = 0.41

Posterior

0.27/0.41 = 0.66

0.14/0.41 = 0.34

0.66 + 0.34 = 1

3. Based on a quick examination, a computer specialist estimates that there is a 0.8 probability that

a computer failure has been caused by a fault in the computer’s motherboard. However an

electronic test, which has a 90% probability of giving a correct indication, and which can be

assumed to be unbiased, indicates that the problem is not caused by the motherboard. The posterior

probability that there is a fault in the motherboard is (to two decimal places):

A) 0.31

B) 0.08

C) 0.26

D) Impossible to calculate based on the info. Given

ANSWER: A) 0.31

Solution

Failure caused by fault in the

computer’s motherboard

Failure is not caused by fault

in the compute’s motherboard

Prior

Conditional

Joint

Posterior

0.80

0.10

0.08

0.31

0.20

0.90

0.18

0.69

0.26

1

4. An economist says that there is “absolutely no chance” of a country’s economy being in a

recession in the las...