# Risk relationships — optional illustrative arithmetic

Subject: Disaster Management

Exam: TEE

Reader: https://deep-learning-study-room.vercel.app/dm/#tee/practice/calculations/risk

Canonical: https://deep-learning-study-room.vercel.app/read/dm/tee/practice/calculations--risk/

Supplementary worked examples · no numerical question found in the available 12 TEE sittings

**Source of the calculations.** M1 PDF p 33 gives probability × impact; pp 34–40 explain disaster-risk components and capacity. All numbers below were authored as illustrations. The actual 1 December 2022 Q2A [10 marks] requires a conceptual explanation and example, not a numerical answer.

**Definition.** Disaster risk is the potential loss associated with a hazardous event and the exposed, vulnerable system. A classroom index can illustrate how hazard, vulnerability and capacity interact; it is not automatically a real probability.

**Simple meaning.** Risk score aur probability alag hain. Formula question mein kaunsa diya hai woh pehle dekho.



$$
R\propto\frac{H\times V}{C}
$$





$$
R_{index}=\frac{H\times E\times V}{C}\quad\text{if exposure is explicitly included}
$$



H is hazard, V vulnerability, E exposure and C capacity. More hazard/exposure/vulnerability generally increases potential loss; stronger capacity can reduce it. Scores must be defined and comparable; do not mix rupees, people and undefined scores and call the result a probability. A separate expected-loss model is probability × consequence when probability and consequence are clearly given.

### Illustrative calculation (not a PYQ). Using the stated classroom index R = HV/C, calculate risk for H = 6, V = 4 and C = 3.

#### Answer

## Given

H=6; V=4; C=3; prescribed index R=HV/C.

## To find

The index value.

## Formula and why



$$
R=HV/C
$$



The question defines this model; it does not supply a separate exposure factor.

## Step-by-step solution

#### Step 1. Multiply hazard and vulnerability



$$
HV=6\times4=24
$$



#### Step 2. Divide by capacity



$$
R=24/3=8
$$



**Final answer:** R=8 index units, not an 8% probability.

#### Illustrative application · Two communities exposed to the same hazard

Two settlements may face similar heavy rain but experience different losses because of drainage, housing, warnings and ability to evacuate. The example separates the hazardous event from exposure, vulnerability and capacity, which together influence disaster risk.

### Illustrative calculation (not a PYQ). In the same model, capacity rises from 3 to 6 while H=6 and V=4 remain unchanged. Find the new index and percentage reduction.

#### Answer

## Given

Old R=8; new C=6; H=6; V=4.

## To find

New R and reduction.

## Formula and why



$$
R=HV/C;\quad \%\text{reduction}=\frac{R_{old}-R_{new}}{R_{old}}100
$$



Only capacity changes, so the inverse relation halves the index.

## Step-by-step solution

#### Step 1. Find new index



$$
R_{new}=(6\times4)/6=4
$$



#### Step 2. Find reduction



$$
8-4=4
$$



#### Step 3. Calculate percentage



$$
(4/8)\times100=50\%
$$



**Final answer:** New index 4; reduction 50%.

#### Illustrative application · Two communities exposed to the same hazard

Two settlements may face similar heavy rain but experience different losses because of drainage, housing, warnings and ability to evacuate. The example separates the hazardous event from exposure, vulnerability and capacity, which together influence disaster risk.

### Illustrative calculation (not a PYQ). A specified damaging event has a 0.1 annual probability and would cause an estimated loss of ₹20 lakh if it occurs. Estimate expected annual loss for this simplified one-event model.

#### Answer

## Given

p=0.1; conditional loss=₹20 lakh.

## To find

Expected annual loss.

## Formula and why



$$
\text{Expected loss}=p\times\text{conditional loss}
$$



Weight the possible consequence by its occurrence probability; this is a different model from an arbitrary risk score.

## Step-by-step solution

#### Step 1. Multiply probability and consequence



$$
0.1\times20=2
$$



#### Step 2. State the interpretation

The result is a long-run expected value under the model, not a prediction that exactly ₹2 lakh will be lost every year.

**Final answer:** ₹2 lakh per year expected loss in the stated model.

#### Practical interpretation · Expected loss is not a yearly bill

A 10% annual probability of a ₹20 lakh loss gives a simplified expectation of ₹2 lakh per year. This is a probability-weighted average for planning, not a prediction that ₹2 lakh will be lost each year or that the event happens exactly once in ten years.

**Yaad rakho:** Hazard and vulnerability up: risk up. Capacity up: risk down.