Probabilities and Expected Values

Question 1

What is the main learning objective of the topic on probabilities and expected values?

Answer 1

Apply probability techniques to improve short-term decision-making with uncertainty

This involves making informed decisions despite lacking complete information.

Question 2

What is the difference between risk and uncertainty?

Answer 2

• Risk: Known probabilities of outcomes
• Uncertainty: Unknown probabilities of outcomes

Risk involves making plans based on known information, while uncertainty involves making plans without sufficient information.

Question 3

Define uncertainty in a business context.

Answer 3

Future outcome is not known and no information is available to evaluate possible outcomes

This is common when a business is embarking on a new venture.

Question 4

What are the two main factors causing uncertainty in the school fundraiser example?

Answer 4

• Unfamiliarity with the nature of the event
• Expansion of the school with new families

These factors make it difficult to predict attendance.

Question 5

Define risk in a business context.

Answer 5

Future outcome is not known, but information is available to evaluate possible outcomes

This typically occurs when replicating current activities.

Question 6

What historical sales data can be used to estimate probability?

Answer 6

• Monthly sales data
• Number of occurrences of each sales volume

This data helps in calculating the likelihood of future sales.

Question 7

Calculate the probability of achieving 100 units in sales based on historical data.

Answer 7

33%

This is derived from 4 occurrences out of 12 total sales.

Question 8

What is the formula for calculating expected value (EV)?

Answer 8

EV = Σpx

Where p is the probability of the outcome and x is the value of that outcome.

Question 9

What are the advantages of using expected values?

Answer 9

• Consolidates data into a single figure
• Simple calculation with historical data

This aids in planning and decision-making.

Question 10

What are the limitations of using expected values?

Answer 10

• Ignores decision maker’s attitude towards risk
• Not suitable for one-off decisions

Expected values represent long-run averages and may not reflect immediate outcomes.

Question 11

If the contribution earned per bag of bagels is $5, what is the expected contribution for 7,207 bags?

Answer 11

$36,035

This is calculated as 7,207 × $5.

Question 12

What happens if Bernie’s produces 7,200 bags but demand is only 7,000 bags?

Answer 12

Total contribution = $34,800

This includes contribution from bags sold minus the cost of unsold bags.

Question 13

What is the expected contribution if production is 7,000 bags each week?

Answer 13

$32,930

This is calculated using the probabilities and contributions from the payoff table.

Question 14

What does the payoff table summarize?

Answer 14

Possible outcomes of production relative to demand

It helps in evaluating the expected value of contributions at different production levels.

Question 15

What is the expected value of contribution for producing 7,400 units?

Answer 15

$35,842

This is the highest expected value of contribution among the production levels considered.

Question 16

What is the formula used to calculate the expected value for a given production level?

Answer 16

Sum of (Probability × Contribution) for each demand level

This formula aggregates the contributions weighted by their probabilities.

Question 17

True or false: The value of perfect information is calculated as EV with perfect information minus EV without perfect information.

Answer 17

TRUE

This calculation helps determine the worth of having accurate demand information.

Question 18

What is the value of perfect information in the scenario described?

Answer 18

$193 per week

This value indicates the maximum Bernie should pay for demand information.

Question 19

If demand is 7,100 bags, what is the best production option for Bernie’s?

Answer 19

Produce 7,100 bags for a contribution of $35,500

This is the optimal production level for that specific demand.

Question 20

What does a higher standard deviation indicate about a project’s outcomes?

Answer 20

Higher risk due to wider dispersion of possible outcomes

Standard deviation measures the variability of returns, impacting risk assessment.

Question 21

What is the average return for both Project A and Project B?

Answer 21

$30,000

Despite having the same average, the projects differ significantly in risk.

Question 22

What is the standard deviation for Project A?

Answer 22

1,414.21

This value indicates low variability in Project A’s possible outcomes.

Question 23

What is the coefficient of variation used for?

Answer 23

To measure relative risk for projects of different sizes

It allows comparison of risk across projects with different average outcomes.

Question 24

What is the expected value for Order 20 in Gerard’s scenario?

Answer 24

$250

This is the highest expected value among the order sizes considered.

Question 25

What is the **formula** for calculating standard deviation?

Answer 25

Square root of (Sum of squared differences / n) ## Footnote This formula quantifies the variability of outcomes.

Question 26

In the context of decision-making, what does **imperfect information** refer to?

Answer 26

Information that has a measure of reliability but is not guaranteed to be accurate ## Footnote It can still provide insights but is less certain than perfect information.

Question 27

What is the **weekly contribution** if demand is 7,000 bags?

Answer 27

$35,000 ## Footnote This is the best outcome for that specific demand level.

Question 28

What does a **narrow range** of possible outcomes indicate about a project?

Answer 28

Lower risk ## Footnote A narrow range suggests less variability and more predictable returns.

Question 29

What is the **total sum of squared differences** for Project B?

Answer 29

$2,032,000,000 ## Footnote This value is used to calculate the standard deviation for Project B.

Question 30

What is the **best production level** for Bernie’s to maximize expected contribution?

Answer 30

7,400 bagels per week ## Footnote This level provides the highest expected contribution based on demand probabilities.

Question 31

What is the **coefficient of variation** used for?

Answer 31

To measure the relative size of the risk for projects with significantly different standard deviations ## Footnote It helps in comparing projects of different sizes.

Question 32

The **coefficient of variation** represents the ratio of the standard deviation to the _______.

Answer 32

mean ## Footnote It is a statistical measure of the dispersion of data points around the mean.

Question 33

True or false: A lower percentage of the **coefficient of variation** indicates higher risk.

Answer 33

FALSE ## Footnote A lower percentage indicates lower risk in comparison with other projects.

Question 34

How is the **coefficient of variation** typically expressed?

Answer 34

As a percentage ## Footnote The percentage helps in understanding the relative risk associated with different projects.

Question 35

What does a higher percentage of the **coefficient of variation** indicate?

Answer 35

Higher risk ## Footnote It confirms that the project has greater variability in its potential outcomes.

Question 36

What is the purpose of using **probabilities** in project evaluation?

Answer 36

To identify past patterns of activity ## Footnote Probabilities help in assessing potential outcomes for decision-making.

Question 37

The concept of **expected values** summarizes possible outcomes into a single average figure for _______.

Answer 37

risk-neutral decision-making ## Footnote This helps in simplifying complex decisions based on multiple outcomes.

Question 38

What role does **information** play in decision-making according to the text?

Answer 38

It improves the quality of decision-making and has a value ## Footnote Better information leads to more informed and effective decisions.

Question 39

The **standard deviation** is used to identify the risk associated with projects that have _______.

Answer 39

a number of possible outcomes ## Footnote It quantifies the variability of potential project results.

Question 40

When comparing projects of different sizes, why can't standard deviations be easily compared?

Answer 40

Because they may not provide a clear indication of risk ## Footnote This is where the coefficient of variation becomes useful.