Page 37 - Applied statistics and probability for engineers

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Probability

An athletic woman in her twenties arrives at the emergency
Chapter Outline department complaining of dizziness after running in hot
weather. An electrocardiogram is used to check for a heart
2-1 Sample Spaces and Events attack, and the patient generates an abnormal result. The test
2-1.1 Random Experiments has a false positive rate 0.1 (the probability of an abnormal
2-1.2 Sample Spaces result when the patient is normal) and a false negative rate
2-1.3 Events of 0.1 (the probability of a normal result when the patient is
2-1.4 Counting Techniques abnormal). Furthermore, it might be assumed that the prior
probability of a heart attack for this patient is 0.001. Although
2-2 Interpretations and Axioms of the abnormal test is a concern, you might be surprised to
Probability learn that the probability of a heart attack given the electro-
2-3 Addition Rules cardiogram result is still less than 0.01. See “Why Clinicians
are Natural Bayesians” (2005, bmj.com) for details of this
2-4 Conditional Probability example and others.
The key is to properly combine the given probabilities.
2-5 Multiplication and Total Probability Furthermore, the exact same analysis used for this medical
Rules example can be applied to tests of engineered products. Con-
sequently, knowledge of how to manipulate probabilities in
2-6 Independence order to assess risks and make better decisions is important
c
2-7 Bayes’ Theorem throughout scientii and engineering disciplines. In this
chapter, the laws of probability are presented and used to
2-8 Random Variables assess risks in cases such as this one and numerous others.

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