Question

Which of the following relationships is/are correct with respect to disaster risk in a geographical location?

• A. Risk = Hazard \(\times\) Vulnerability \(\times\) Exposure \(\times\) Capacity
• B. Hazard = Risk \(\times\) Capacity \(\times\) Exposure
• C. Risk = (Hazard \(\times\) Vulnerability \(\times\) Exposure) / Capacity
• D. Exposure = (Hazard \(\times\) Vulnerability) / Risk

Hint:

The standard disaster risk formula is Risk = (Hazard x Vulnerability x Exposure) / Capacity; capacity reduces risk, so it belongs in the denominator, never multiplied in.

Answer 1

The Correct Option is C

Step 1: State the standard disaster risk formula.
Disaster risk management defines risk with four factors: Hazard (\(H\)), the chance and strength of a damaging event; Exposure (\(E\)), the people and assets that are in the hazard's path; Vulnerability (\(V\)), how easily those people and assets are harmed; and Capacity (\(C\)), the ability of the community to cope with and recover from the event.
The accepted relationship, used by UNDRR and similar disaster risk frameworks, is
\[ \text{Risk} = \frac{\text{Hazard} \times \text{Vulnerability} \times \text{Exposure}}{\text{Capacity}} \]
Risk rises when hazard, vulnerability or exposure rises, and it falls when the community's coping capacity rises, which is why capacity sits in the denominator, not multiplied into the numerator.

Step 2: Test option (A).
Option (A) writes Risk = Hazard \(\times\) Vulnerability \(\times\) Exposure \(\times\) Capacity, with capacity multiplied in. That would mean a higher coping capacity always makes the risk bigger, which is the opposite of what capacity actually does. So (A) is wrong.

Step 3: Test option (B).
Rearranging the correct formula for Hazard gives \(H = \dfrac{\text{Risk} \times \text{Capacity}}{\text{Vulnerability} \times \text{Exposure}}\), which needs Vulnerability in the denominator. Option (B), Hazard = Risk \(\times\) Capacity \(\times\) Exposure, multiplies Capacity and Exposure into the numerator and drops Vulnerability entirely, so it does not match. (B) is wrong.

Step 4: Test option (C).
Option (C) writes Risk = (Hazard \(\times\) Vulnerability \(\times\) Exposure) / Capacity, which is exactly the standard formula from Step 1. So (C) is correct.

Step 5: Test option (D).
Rearranging the correct formula for Exposure gives \(E = \dfrac{\text{Risk} \times \text{Capacity}}{\text{Hazard} \times \text{Vulnerability}}\). Option (D) instead writes Exposure = (Hazard \(\times\) Vulnerability) / Risk, which has Capacity missing and Risk placed in the wrong position. So (D) is wrong.

Final Answer:
Only option (C) states the correct relationship. \[ \boxed{\text{Risk} = \dfrac{\text{Hazard} \times \text{Vulnerability} \times \text{Exposure}}{\text{Capacity}}} \]