A junior project manager designs a decision tree for a critical path activity. The chance node features two possible branches: Path A with a 60% probability and a $10,000 impact, and Path B with a 50% probability and a $20,000 impact. What is the fundamental mathematical error in this model?

The branch probabilities at the chance node do not sum to 1.0

The decision nodes incorrectly incorporated qualitative risk assessment scoring

The expected monetary values were not converted to positive integer values

The risk financial impacts were calculated using management reserve funding

A risk register entry lists only the risk statement. Which missing data blocks decision-tree analysis and what must be requested?

Missing residual probability and impact; request both values plus response cost

Missing mitigation; request response strategy

Missing trigger; request monitoring plan

Missing root cause; request cause analysis

A project manager treats a low-probability event as certain and halts all work. Which flaw exists in this reasoning and what corrective step is required?

Failed to weight event by probability

Ignored high-probability low-impact risks

Applied risk acceptance appropriately

Used expected monetary value correctly

Daily burn rate is $45,000. A regulatory delay adds 12 days and $180,000 rework. Calculate total monetary impact and EMV if probability is 0.4.

Total impact $720,000; EMV $288,000

Total impact $540,000; EMV $216,000

Total impact $900,000; EMV $360,000

Total impact $720,000; EMV $720,000

Two mutually exclusive vendor mitigation paths are evaluated. Vendor A has a baseline cost of $50,000 and a 20% probability of failure causing a $100,000 impact. Vendor B has a baseline cost of $60,000 and a 10% probability of failure causing a $150,000 impact. Which vendor should be selected under risk-neutral assumptions, and what is the expected cost?

Vendor A with an expected cost of $70,000

Vendor B with a total expected cost of $75,000

Vendor B with a total expected cost of $210,000

Vendor A with a total expected cost of $150,000

2.3.3.2

Concept · under Risks, issues and impediments

Expected monetary value and decision trees for the PMP® exam

Expected monetary value (EMV) is probability times impact: a risk with a 35% chance of costing $24,000 has an EMV of −$8,400. Threats carry a negative sign and opportunities a positive one, and a decision tree adds those weighted values along each path so you can compare the choices.

Exam: PMP
Domain: Business Env.
Domain weight: 26%
Packages: 8
Updated: Oct 13, 2026

01The formula and its signs

Expected monetary value

EMV=P × I

P: probability that the risk occurs, written as a decimal between 0 and 1
I: impact in money if it does: negative for a threat, positive for an opportunity

Worked example

P threat = 0.35
I threat = −$24,000
P opportunity = 0.16
I opportunity = +$40,000

Threat: 0.35 × −24,000 = −8,400.
Opportunity: 0.16 × 40,000 = +6,400.
Net exposure of the pair: −8,400 + 6,400 = −2,000.

Net EMV = −$2,000

Reading itExpect to lose about $2,000 on these two risks taken together. It is an average over many possible outcomes; on one real project the threat either happens in full or not at all.

02Is a response worth its price?

EMV belongs to quantitative risk analysis, part of risks, issues and impediments, and it earns its keep when you set it against what a response costs. Take the threat above. A $3,000 response that cuts its probability from 0.35 to 0.12 leaves a residual EMV of 0.12 × −24,000 = −2,880. Response plus residual comes to −5,880, against −8,400 for doing nothing, so the response is ahead by $2,520 in expected terms.

Added up across the risk register, EMVs also inform the contingency reserve inside the cost baseline, which is where this topic meets budget, reserves and earned value. Which response to pick in the first place is a separate decision, covered in risk response strategies.

03A decision tree, written out

Build in-house or buy a fixed-price module: expected cost of each path (our own numbers)

Path	Up-front cost	Chance node	Weighted outcome	Expected cost
Build in-house	$68,000	0.45 chance of a $17,000 overrun, 0.55 chance of none	0.45 × 17,000 = 7,650	$75,650
Buy the module	$82,000	0.14 chance of $12,000 in integration fixes, 0.86 chance of none	0.14 × 12,000 = 1,680	$83,680

The tree is written in costs, so the smaller expected cost wins: build in-house at $75,650. Drop the module's price to $73,000 and the answer flips, because buying would then come to $74,680. A tree written in payoffs works the other way round: pick the largest value.

04What a Monte Carlo run adds

A Monte Carlo simulation runs the schedule or cost model thousands of times, drawing each duration or cost from the range the team estimated, often the three-point ranges described in PERT and three-point estimating, and switching identified risks on or off at their probabilities. What comes out is a distribution instead of one number, plus a view of which inputs move the result most, which shows where a response buys the most certainty.

The distribution is read as confidence levels: P80 is the value that 80% of runs came in at or under. The single most likely value from a three-point estimate often sits below the P50, because project ranges usually stretch further on the late or expensive side. Which level to commit to is the sponsor's call: P80 buys more certainty than P50 at the price of a later date or a larger reserve.

05Run the numbers

Arithmetic and judgment both show up here: a calculation in some items, the meaning of an EMV figure in others.

Work packages 8

WP 01A junior project manager designs a decision tree for a critical path activity. The chance node features two possible branches: Path A with a 60% probability and a $10,000 impact, and Path B with a 50% probability and a $20,000 impact. What is the fundamental mathematical error in this model?
Debrief answer to open the notes
1. ACorrect: branches from a chance node are mutually exclusive and must sum to 1.0; here 0.6 + 0.5 = 1.1, so the expected values are invalid.
2. BNo qualitative scores are described; the error is in the probabilities.
3. CEMV can be negative for threats; there is no need to convert values to positive integers.
4. DThe funding source does not affect the branch math, and nothing indicates management reserve was used.
More notes below ↓
WP 02A risk register entry lists only the risk statement. Which missing data blocks decision-tree analysis and what must be requested?
Debrief answer to open the notes
1. AA response strategy is useful but cannot be valued in a tree without probability and impact.
2. BTriggers support monitoring, not the expected-value calculation.
3. CRoot cause informs responses but is not a numeric input to the tree.
4. DCorrect: a decision tree needs probability and impact for each branch plus the cost of each response to compare expected values.
More notes below ↓
WP 03A critical vendor faces end-of-life risk with 25% probability and $800k impact. Mitigation costs $150k. What is the EMV of doing nothing and the recommended action?
Debrief answer to open the notes
1. A$50k is not 25% of $800k, and accepting a $200k expected loss is hard to justify when mitigation costs less.
2. B$150k is the mitigation cost, not the EMV of doing nothing.
3. C$950k adds impact and mitigation cost; EMV weights impact by probability.
4. DCorrect: EMV = 0.25 × −$800k = −$200k for this threat (the options quote the magnitude); mitigation at $150k costs less than the expected loss it addresses.
More notes below ↓
WP 04A project manager treats a low-probability event as certain and halts all work. Which flaw exists in this reasoning and what corrective step is required?
Debrief answer to open the notes
1. AThe scenario concerns a low-probability event, not neglected high-probability risks.
2. BHalting all work is not acceptance; acceptance would mean continuing and monitoring.
3. CCorrect: risk exposure is probability times impact; treating a low-probability event as certain overstates it, so weight it by its probability.
4. DEMV weights by probability, which is exactly what was not done here.
More notes below ↓
WP 05Daily burn rate is $45,000. A regulatory delay adds 12 days and $180,000 rework. Calculate total monetary impact and EMV if probability is 0.4.
Debrief answer to open the notes
1. A$540,000 counts only the delay cost (12 × $45,000) and leaves out the $180,000 rework.
2. BCorrect: impact = 12 × $45,000 + $180,000 = $720,000, so EMV = 0.4 × −$720,000 = −$288,000 for this threat; the options quote magnitudes.
3. C$900,000 overstates the impact; 12 days at $45,000 plus rework is $720,000.
4. DThe impact is right, but the EMV ignores the 0.4 probability.
More notes below ↓
WP 06A project team has identified a risk of material shortages that could impact the project schedule. The probability of this risk occurring is 30%, and the potential impact is a 2-week delay valued at $60,000. What is the Expected Monetary Value (EMV) of this risk?
Debrief answer to open the notes
1. A$60,000 is the full impact if the risk occurs, not its expected value.
2. BCorrect: EMV = 0.30 × −$60,000 = −$18,000 for this threat; the options give the magnitude.
3. C$20,000 does not match probability times impact for these values.
4. D$30,000 would imply a 50% probability.
More notes below ↓
WP 07Two mutually exclusive vendor mitigation paths are evaluated. Vendor A has a baseline cost of $50,000 and a 20% probability of failure causing a $100,000 impact. Vendor B has a baseline cost of $60,000 and a 10% probability of failure causing a $150,000 impact. Which vendor should be selected under risk-neutral assumptions, and what is the expected cost?
Exhibit for WP 07
Vendor Baseline Cost Failure Probability Failure Impact
Vendor A $50,000 20% $100,000
Vendor B $60,000 10% $150,000
Debrief answer to open the notes
1. A$75,000 is Vendor B's expected cost, 60,000 + 0.10 x 150,000, which is higher than Vendor A's.
2. B$210,000 adds B's full failure impact to its baseline, ignoring the 10% probability.
3. CCorrect: Vendor A = 50,000 + 0.20 x 100,000 = $70,000; Vendor B = 60,000 + 0.10 x 150,000 = $75,000, so A is lower.
4. D$150,000 adds A's full impact to its baseline; expected cost weights the impact by its 20% probability.
More notes below ↓
WP 08A risk mitigation decision uses EMV analysis. Baseline: mitigation cost $40k, failure probability 0.25 with $200k impact. Sensitivity shows at what probability threshold the decision flips?
Exhibit for WP 08
Scenario Probability Impact ($k) EMV ($k) Mitigation Cost ($k) Net Value
Baseline 0.25 200 50 40 10
Alt 1 0.18 200 36 40 -4
Alt 2 0.30 200 60 40 20
Debrief answer to open the notes
1. AAt 0.25 the risk EMV is $50k, still above the $40k cost, so the decision has not flipped yet.
2. BAt 0.15 the EMV is $30k, already below the cost; the break-even point is higher than this.
3. CCorrect: mitigation pays off while P x 200k exceeds the 40k cost. Break-even is 40 / 200 = 0.20; below it, accept the risk.
4. DAt 0.30 the EMV is $60k and mitigation is clearly worth it; this is not where the decision changes.
More notes below ↓

Vendor	Baseline Cost	Failure Probability	Failure Impact
Vendor A	$50,000	20%	$100,000
Vendor B	$60,000	10%	$150,000

Scenario	Probability	Impact ($k)	EMV ($k)	Mitigation Cost ($k)	Net Value
Baseline	0.25	200	50	40	10
Alt 1	0.18	200	36	40	-4
Alt 2	0.30	200	60	40	20

Open a row to answer. Keys: 1–4 or A–D answer, N opens the next row.

06Signs, scores and simulations

Is EMV the same thing as a risk score?

A probability and impact score ranks risks on a scale, usually during qualitative analysis. EMV puts money on each risk, which is what lets you add risks together and set them against the cost of a response.

Why does an opportunity get a positive EMV?

Because it adds value if it happens. Keeping the signs straight lets a decision tree net threats against opportunities on the same path.

How much Monte Carlo math do you need to do yourself?

Very little arithmetic: the simulation does it. What matters is reading the output, such as what a confidence level means.