Expected Value Flashcards
The probabilities shown in the table below represent the estimate of sales for a
new product.
Sales (Units) Probability
0-200 15%
201-400 45%
401-600 25%
601-800 5%
Question: 1What is the probability of selling between 201 and 600 units of the product?
A. 0%
B. 11.25%
C. 70%
D. 25%
Answer (C) is correct.
The probability of selling between 201 and 400 units is 45%, and the probability of selling between
401 and 600 units is 25%. Hence, the probability of selling between 201 and 600 units is the sum of
these probabilities, or 70%.
The probabilities shown in the table below represent the estimate of sales for a
new product.
Sales (Units) Probability
0-200 15%
201-400 45%
401-600 25%
601-800 15%
Question: 2What is the best estimate of the expected sales of the new product?
A. 480
B. 380
C. 400
D. 800
Answer (B) is correct.
The expected sales levels should be weighted by the individual probabilities of their occurrence. The
midpoint of each sales level is used as the estimate for that level. Thus, sales are expected to be 380
units.
100 × 15% = 15
300 × 45% = 135
500 × 25% = 125
700 × 15% = 105
380
3In decision making under conditions of uncertainty, expected value refers to the
A. Likely outcome of a proposed action.
B. Present value of alternative actions.
C. Probability of a given outcome from a proposed action.
D. Weighted average of probable outcomes of an action.
Answer (D) is correct.
The expected value of an action is found by multiplying the probability of each possible outcome by its
payoff and summing the products. It represents the long-term average payoff for repeated trials. In
other words, expected value is the weighted average of probable outcomes.
A beverage stand can sell either soft drinks or coffee on any given day. If the
stand sells soft drinks and the weather is hot, it will make $2,500; if the weather is cold, the
profit will be $1,000. If the stand sells coffee and the weather is hot, it will make $1,900; if the
weather is cold, the profit will be $2,000. The probability of cold weather on a given day at this
time is 60%.
Question: 4If the probability of hot weather, given a hot weather forecast, is 50%, how much would the vendor
be willing to pay for the forecast?
A. $600
B. $300
C. $1,000
D. $500
Answer (B) is correct.
If the weather is hot and coffee is served, the vendor earns $1,900. If the vendor knows the weather
will be hot, (s)he would sell soft drinks and make $2,500, a $600 increase. Thus, the vendor should be
willing to pay up to $600 for perfect information regarding hot weather. However, if the forecasts are
only 50% accurate, the information is not perfect. Accordingly, the vendor should be willing to pay
only $300 (the $600 potential increase in profits × 50%) for the sometimes accurate forecasts.
Butler and Burnside are projecting market conditions for the upcoming month.
T hey have prepared the following payoff table:
Demand in Units
0 2 4 6
Probability of Demand
Supply 0.1 0.3 0.4 0.2
in Units
0 $ 0 $ 0 $ 0 $ 0
2 (80) 40 40 40
4 (160) (40) 80 80
6 (240) (120) 0 120
Question: 7The price Butler and Burnside are willing to pay for perfect information is
A. $68
B. $40
C. $48
D. $104
Answer (B) is correct.
The maximum amount the seller should pay for perfect information is the difference between the
expected profit with perfect information and the expected profit if demand is not known. With perfect
information, supply is the correct amount of units to maximize profit at each level of demand. Thus,
the expected profit with perfect information is computed as follows:
Demand Supply Payoff Probability Weighted
Payoffs
0 0 $ 0 × .1 = $ 0
2 2 40 × .3 = 12
4 4 80 × .4 = 32
6 6 120 × .2 = 24
Expected Profit
$68
Without perfect information, the seller should purchase the supply that will result in the maximum
long-run profit. Using the information given, it can be determined that the profit will be $20 when the
supply is 4 units. It is also evident that the profit is zero when the supply is zero. The expected profit
must also be calculated for supply levels of 2 and 6 units. For a supply of 2 units, the expected profit is
.1(–$80) + .3($40) + .4($40) + .2($40) = $28
For a supply of 6 units, the expected loss is
.1(–$240) + .3(–$120) + .4($0) + .2($120) = $(36)
Thus, without perfect information, profits are maximized at $28 when the supply is 2 units. However,
with perfect information, profits will be $68. Thus, a rational seller should therefore be willing to pay
up to $40 ($68 – $28).
Question: 8A company’s managers are attempting to value a piece of land they own. One potential occurrence is
that the old road bordering the land gets paved. Another possibility is that the road does not get paved. A third
outcome is that the road might be destroyed and completely replaced by a new road. Based on the following future
states of nature, their probabilities, and subsequent values of the land, what is the expected value of the land?
Future States of Nature (SN)
Probability
SN 1: Current road gets paved .5
SN 2: Road does not get paved .4
SN 3: Current road destroyed and
replaced with new road .1
Estimates of land value under each possible future state of nature:
Value if SN 1: $200,000
Value if SN 2: $100,000
Value if SN 3: $550,000
A. $133,333
B. $195,000
C. $225,000
D. $283,333
Answer (B) is correct.
The expected value of the land is determined by multiplying the probability of each state of nature by
the value under that particular state of nature and adding all of the products. Thus, the land’s expected
value is $195,000 [(0.5)($200,000) + (0.4)($100,000) + (0.1)($550,000)].
15A company is in the process of preparing its budget. As part of the process, the company has
prepared sales estimates and estimated the probability associated with each sales estimate. Which one of the
following techniques should be used by the company to determine sales for budgeting purposes?
A. Linear programming.
B. Minimax regret criteria.
C. Expected value analysis.
D. Monte Carlo simulation
Answer (C) is correct.
The expected value of an action is found by multiplying the probability of each possible outcome by its
payoff and summing the products. It represents the long-term average payoff for repeated trials. If
estimates of sales and probabilities are known, expected value analysis can be used to determine
budgeted sales.
16The expected monetary value of an event
A. Is equal to the conditional value or profit of the event.
B. Is equal to the payoff of the event times the probability the event will occur.
C. Is the profit forgone by not choosing the best alternative.
D. Is the absolute profit from a particular event.
Answer (B) is correct.
For decisions involving risk, the concept of expected value provides a rational means for selecting the
best alternative. The expected value of a decision is found by multiplying the probability of each
outcome by its payoff, and summing the products. The result is the long-term average payoff for
repeated trials.
17Expected value in decision analysis is
A. A standard deviation using the probabilities as weights.
B. An arithmetic mean using the probabilities as weights.
C. The square root of the squared deviations.
D. A measure of the difference between the best possible outcome and the outcome of the original decision.
Answer (B) is correct.
Expected value analysis is an estimate of future monetary value based on forecasts and their related
probabilities of occurrence. The expected value is found by multiplying the probability of each
outcome by its payoff and summing the products. Expected value is thus an arithmetic mean using
probabilities as weights.
22The expected monetary value of an act is the
A. Sum of the conditional profit (loss) for each event.
B. Sum of the conditional profit (loss) for each event times the probability of each event’s occurrence.
C. Conditional profit (loss) for the best event times the probability of each event’s occurrence.
D. Revenue minus the costs for the act.
Answer (B) is correct.
Expected value analysis estimates future monetary value based on forecasts and their related
probabilities of occurrence. The expected value under uncertainty is found by multiplying the
probability of each outcome (event) by its payoff (conditional profit or loss) and summing the
products.
23The expected value of perfect information is the
A. Same as the expected profit under certainty.
B. Sum of the conditional profit (loss) for the best event of each act times the probability of each event
occurring.
C. Difference between the expected profit under certainty and the expected opportunity loss.
D. Difference between the expected profit under certainty and the expected monetary value of the best act
under uncertainty.
Answer (D) is correct.
Perfect information permits certainty that a future state of nature will occur. The expected value of
perfect information determines the maximum amount a decision maker is willing to pay for
information. It is the difference between the expected value without perfect information, that is, the
expected value of the best action under uncertainty and the expected value under certainty. Under
certainty, a decision maker knows in each case which state of nature will occur and can act
accordingly.
24In decision theory, those uncontrollable future events that can affect the outcome of a decision are
A. Payoffs.
B. States of nature.
C. Probabilities.
D. Nodes.
Answer (B) is correct.
Applying decision theory requires the decision maker to develop an exhaustive list of possible future
events. All possible future events that might occur must be included, even though the decision maker
will likely be very unsure as to which specific events will occur. These future uncontrollable events are
referred to as states of nature.
The Booster Club at Blair College sells hot dogs at home basketball games. The
group has a frequency distribution of the demand for hot dogs per game and plans to apply the
expected value decision rule to determine the number of hot dogs to stock.
Question: 25The Booster Club should select the demand level that
A. Is closest to the expected demand.
B. Has the greatest probability of occurring.
C. Has the greatest expected opportunity cost.
D. Has the greatest expected monetary value.
Answer (D) is correct.
The Booster Club should select the demand level that maximizes profits, that is, the level with the
greatest expected monetary value. This level may not include the event with the highest conditional
profit because this profit may be accompanied by a low probability of occurrence. Alternatively, the
event with the highest probability of occurrence may not be selected because it does not offer a high
conditional profit.
A company is considering three alternative machines to produce a new product.
The cost structures (unit variable costs plus avoidable fixed costs) for the three machines are
shown as follows. The selling price is unaffected by the machine used.
Single purpose machine $.60x + $20,000
Semiautomatic machine $.40x + $50,000
Automatic machine $.20x + $120,000
The demand for units of the new product is described by the following probability distribution.
Demand Probability
200,000 0.4
300,000 0.3
400,000 0.2
500,000 0.1
Question: 27Using the expected value criterion,
A. The single purpose machine should be used because of the low expected demand.
B. The automatic machine should be used because of the high expected demand.
C. The semiautomatic machine should be used because it has the lowest expected cost.
D. The automatic machine has the lowest expected cost.
Answer (C) is correct.
The semiautomatic machine has an expected cost of $170,000 based on an expected demand of
300,000 units [(.4 × 200,000) + (.3 × 300,000) + (.2 × 400,000) + (.1 × 500,000)]. The single purpose
machine has an expected cost of $200,000 [($.60 × 300,000) + $20,000]. The automatic machine has
an expected cost of $180,000 [($.20 × 300,000) + $120,000)]. Hence, the semiautomatic machine has
the lowest expected cost at the expected level of demand.
A computer store sells four computer models designated as P104, X104, A104,
and S104. The store manager has made random number assignments to represent customer
choices based on past sales data. The assignments are shown below.
Model
Random Numbers
P104 0-1
X104 2-6
A104 7-8
S104 9
Question: 31The probability that a customer will select model P104 is
A. 10%
B. 20%
C. 50%
D. Some percentage other than those given.
Answer (B) is correct.
Ten random numbers have been assigned. Of these, two (0 and 1) have been assigned to model P104.
Thus, there are two chances out of ten, or 20%, that a customer will select that model.
