Final Answer:
Risk management that halves the probability while keeping the impact constant results in a 50% reduction in overall risk. This is due to the direct relationship between probability, impact, and overall risk in risk management calculations. Thus the correct option is C. 50%.
Step-by-step explanation:
Risk management that cuts the Probability in half with no Impact change will reduce the overall risk level by 50%. This is because risk is a combination of probability and impact, and cutting the probability in half directly reduces the overall risk by that proportion.
In risk management, the overall risk (R) is calculated as the product of the probability (P) and the impact (I): R = P × I. If we reduce the probability by half, the new risk becomes R' = (P/2) × I. To find the percentage reduction in risk, we compare the original risk to the new risk:
![\[ \text{Percentage Reduction} = (R - R')/(R) * 100 \]](https://img.qammunity.org/2024/formulas/business/college/6q43f5oy46lhgydx4m70rm4qja8q1zjunx.png)
Substituting the expressions for R and R', we get:
![\[ \text{Percentage Reduction} = (P * I - (P)/(2) * I)/(P * I) * 100 \]](https://img.qammunity.org/2024/formulas/business/college/ejgl54cql4fbduz7t4ubhy0kciyetm7ozh.png)
Simplifying further:
![\[ \text{Percentage Reduction} = ((P)/(2) * I)/(P * I) * 100 \]](https://img.qammunity.org/2024/formulas/business/college/1fvw1oz85cn5chmgwdp89d9xnhvldwxf40.png)
![\[ \text{Percentage Reduction} = (1)/(2) * 100 \]](https://img.qammunity.org/2024/formulas/business/college/b6c5myi20uy82guee7l8tgsxoilcik38o4.png)
Reducing the probability component of risk by half without changing the impact directly translates to a 50% reduction in overall risk. This highlights the importance of effective risk management strategies in minimizing potential negative outcomes.
Therefore, the risk reduction is 50%. So, the final answer is C. 50%.