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Understanding Cumulative Risk

To make good decisions, people need to be able to understand the risks that exist and how they accumulate over time.  Most people cannot accurately answer the (simple) questions below because cumulative risk judgments are hard. 

A small difference in short-term risk can become significant in the long term. Suppose you are trying to decide between two drugs to reduce blood pressure, and both have a harmful side effect. The risk of harm from Drug A is 1% over a year—that is, on average only 1 person out of every 100 using the drug for a year should suffer the side effect. The risk of harm from Drug B is 3% over a year. 

The difference may seem negligible. But the cumulative risks of experiencing the side effect at least once over 10 years differ markedly for the two drugs: 10% for Drug A and 26% for Drug B.  Now suppose you are given a drug that has a risk of a harmful side effect of 5% in a year. What are the chances that you will not experience the harmful side effect if you take the drug for a period of five years? The question calls for an estimate of a cumulative risk (scroll down for the answer). Most people find such problems very difficult. Consider the question from another angle: What are the chances that you will experience the harmful side effect at least once in the five-year period? (again, scroll down for the answer). Cumulative-risk judgements are hard.

How to improve your ability to judge cumulative risk: break the problem down into several iterative steps (oh, and make the arithmetic simple because people are increasing innumerate).

This paper summarizes the theory of simple cumulative risks—for example, the risk of food poisoning from the consumption of a series of portions of tainted food. Problems concerning such risks are extraordinarily difficult for na ̈ıve individuals, and the paper explains the reasons for this difficulty. It describes how na ̈ıve individuals usually attempt to estimate cumulative risks, and it outlines a computer program that models these methods. This account predicts that estimates can be improved if problems of cumulative risk are framed so that individuals can focus on the appropriate subset of cases. The paper reports two experiments that corroborated this prediction. They also showed that whether problems are stated in terms of frequencies (80 out of 100 people got food poisoning) or in terms of percentages (80% of people got food poisoning) did not reliably affect accuracy.

Source:Understanding cumulative risk (paper)

Answers:
1. There is a 78% chance that the harmful side effect will not occur over five years. 
2. The answer is 22%.