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# hw4 - CS 440 Introduction to AI Homework 4 Due November 9...

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CS 440: Introduction to AI Homework 4 Due: November 9 11:59PM, 2010 Your answers must be concise and clear. Explain sufficiently that we can easily determine what you understand. We will give more points for a brief interesting discussion with no answer than for a bluffing answer. Please email your solution to the TA at [email protected] 1 Probability 1. Consider a joint probability distribution P ( X, Y, Z ) over variables X, Y, and Z. Assume that the probability of each outcome is non-zero. Is the following equation always true? Prove its correctness or incorrectness. P ( X | Y, Z ) = P ( Y | X,Z ) P ( X | Z ) P ( Y | Z ) 2. After your yearly checkup, the doctor has bad news and good news. The bad news is that you tested positive for a serious disease and that the test is 95% accurate (i.e., the probability of testing positive when you have the disease is 0.95 and the probability of testing negative when you don’t have the disease is 0.95). The good news is that this is a rare disease, striking only 1 in 100,000 individuals. Why is it good news that the disease is rare? What are the chances that you actually have the disease?

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