The following Guest article is an extract from the book Project Decisions: The Art and Science By authors Lev Virine and Michael Trumper, published by Management Concepts, Inc.© 2008. Reproduced with permission. Published here July 2008.

## Answers to Questions 1 to 4

1.   The correct answer is C (63 days). You cannot add high estimates (40 days + 40 days = 80 days) together to get the duration of the project with two activities associated with 90% confidence. It cannot be 50 days ( 2*(10 days + 40 days)/2), which is the mean duration. The actual calculation can be performed using quantitative analysis tools based on Monte Carlo simulations. For more information please read Chapter 16, "What Is Project Risk?" or "PERT and Monte Carlo."

2.   The correct answer is B (Strategy B is 17% faster than strategy A).
A similar example is discussed in Chapter 20, "Adaptive Project Management." Splitting a risky project into smaller phases usually accelerates the project, but not as significantly as 70%. An actual calculation can be performed using event chain methodology.

3.   The correct answer is C (portrait completion times in situations A and B are about the same). The correlation between risk events plays a significant role only if probabilities are relatively high. In this case, the probability that Katie or Tom will not like the portrait is 30%; therefore, correlations will not have a significant effect on the results. See Chapter 14, "What Is Most Important: Sensitivity Analysis and Correlations."

4.   The correct answer is C (4%). This question is related to the psychological bias called ignoring base rate frequencies. See Chapter 13, "Estimating Probabilities." According to the Bayes theorem, the probability of defective amplifiers is:

P(defective|positive test) = P(positive test|defective) P(defective) P(positive test|defective) P(defective) + P(positive test|not defective) P(not defective)

Where: P(defective) = probability of defective amplifiers (0.01) P(not defective) = probability of nondefective amplifiers (0.99) P(positive test|defective) = probability of positive test indicating that amplifier is defective (0.8) P(positive test|not defective) = probability of positive test indicating that amplifier is not defective (0.2) = false positive

Sign "|" means "given"

P(defective| positive test) = 0.8*0.01/(0.8*0.01 + 0.2 *0.99) = 0.0388 ~ 4%

Sometimes people pay too much attention to the number associated with the accuracy of the test, which becomes an anchor. However, the original probability of failure (1%) is the most important value in this equation.