Disaster Management · TEE · practice

Risk relationships — optional illustrative arithmetic

Optional calculation practice

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}LaTeX: R\propto\frac{H\times V}{C}
R_{index}=\frac{H\times E\times V}{C}\quad\text{if exposure is explicitly included}LaTeX: 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/CLaTeX: 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=24LaTeX: HV=6\times4=24

Step 2. Divide by capacity

R=24/3=8LaTeX: R=24/3=8

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

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}}100LaTeX: 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=4LaTeX: R_{new}=(6\times4)/6=4

Step 2. Find reduction

8-4=4LaTeX: 8-4=4

Step 3. Calculate percentage

(4/8)\times100=50\%LaTeX: (4/8)\times100=50\%

Final answer: New index 4; reduction 50%.

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}LaTeX: \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=2LaTeX: 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.

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