SCIENCE · INVESTIGATE AND EXPLAIN

Separate overlapping hazard events from expected consequences

Hazard describes a potentially damaging process and its occurrence or intensity; exposure identifies what lies in its path, and vulnerability concerns how those exposed things respond. A geological susceptibility map is not automatically a calibrated annual probability map, nor does identical hazard imply identical consequences for different sites.

Learning outcome: Check the complete probability partition before calculating loss. Vary intersection at a fixed joint consequence, then vary consequence at fixed probabilities. Explain why probability, exposed value and expected loss cannot share one unlabeled axis.

Starting recap

Retain resource inventories, physical force and reaction boundaries, chronological alternatives and explicit decision constraints. Conditional teaching results do not certify actual site suitability.

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Try

At intersection 0.05 and joint loss 80, state probabilities are 0.75,0.15,0.05,0.05. At least one event has probability 0.25; expected loss is 0.15×40+0.05×60+0.05×80=13 million units/year. Independence would instead require intersection 0.02.

Open the experiment

Predict

Can changing dependence alter the event-union probability even when both marginal probabilities stay fixed?

Your prediction and reason

Experiment

Check the complete probability partition before calculating loss. Vary intersection at a fixed joint consequence, then vary consequence at fixed probabilities. Explain why probability, exposed value and expected loss cannot share one unlabeled axis.

Retain overlapping-event probability and capped losses

Worked teaching model · synthetic values · Fictional annual states: P(flood)=0.2, P(slide)=0.1, intersection a. Flood-only loss 40, slide-only 60, both loss b. States are exclusive after partitioning. Supplied joint loss need not equal the sum because assets may overlap. Not actual hazard calibration or monetary advice.

Joint flood-and-slide probability: 0.05 fraction per year Joint-state loss: 80 million fictional units

Reset keeps your prediction, captures and practice history.

Adding marginal probabilities double-counts the joint state.

Expected loss uses exhaustive mutually exclusive states. Dependence can change event-union probability and overlap consequences; probability is not loss, and one average does not represent tail severity, distributional equity or a forecast of next year.

Neither: Probability 0.75; conditional loss 0

Flood only: Probability 0.15000000000000002; conditional loss 40

Slide only: Probability 0.05; conditional loss 60

Both: Probability 0.05; conditional loss 80

Complete conditional quantities, with separate units
Quantity	Value	Unit
At least one event	0.2500000	probability
Expected flood-only loss	6.000000	million units/year
Expected slide-only loss	3	million units/year
Expected joint-state loss	4	million units/year
Total expected loss	13	million units/year
Joint probability if independent	0.02000000	probability

Original instructional packets and diagrams, not actual site measurements, legal limits or professional clearance.

Adding marginal probabilities double-counts the joint state.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

1. Define the evidence and process

2. Connect mechanism, geometry and boundary

The fictional annual probabilities are 0.2 for a flood and 0.1 for a slide. Their intersection a is supplied separately rather than assumed independent. Partition the possibilities into neither with probability 0.7+a, flood only 0.2−a, slide only 0.1−a, and both a. These nonnegative, mutually exclusive states sum to one. The event-union probability is 0.3−a.

Stipulated losses are 40 million units for flood only, 60 for slide only and b for the joint state. The joint loss may be below 100 because both hazards can affect overlapping assets; it is not automatically the sum of two standalone losses. Expected loss is the sum of each state probability times its own conditional loss, with the no-event state contributing zero.

Expected loss is a long-run average within the model, not a prediction that one year will experience that exact amount. It hides the distribution of severe outcomes, unequal impacts and nonmonetized values. Dependence, exposure and loss functions require distinct evidence; this fictional calculation neither prices a real community nor supplies operational warnings.

3. Reconstruct the worked packet

4. Predict and investigate

Predict first: Can changing dependence alter the event-union probability even when both marginal probabilities stay fixed?

5. Test changed evidence

Apply the evidence to a changed case

With intersection 0.1 and joint loss 60, calculate the union probability and expected loss.

Retain the evidence frame, calculations and assumptions before opening public feedback.

Compare a worked response

Union probability is 0.2; states are neither 0.8, flood-only 0.1, slide-only 0, both 0.1. Expected loss is 4+0+6=10 million units/year. Every slide coincides with a flood in this supplied distribution; that is not independence.

6. Retain a bounded decision

Preserve the first plan, source identity, original observations, units and competing interpretations. All numerical packets and diagrams in this category are invented teaching cases, not measured site conditions. Retain earlier actual USGS archives separately; do not merge unrelated sites into an invented actual history. Human review, unfamiliar transfer and any chosen supervised practical pathway remain separate. No mining, treatment, slope access or environmental clearance is authorized by these exercises.

Mechanism reference, checked 30 October 2026. Original prose, calculations, questions and diagrams.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

With intersection 0.1 and joint loss 60, calculate the union probability and expected loss.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Resolve effective normal force before interpreting slope resistance Next: Close weathering and carbonate burial across a geological carbon boundary

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