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Q-4: Inference. A student of the Machine Learning class notices that people driving SUV (S) consume large amounts of gas (G) and are involved in more accidents than the national average (A). He also noticed that there are two types of people that drive SUVs: people from Pennsylvania (L) and people with large families (F). After collecting some statistics, he arrives at the following Bayesian network. P(L)-0.4 L F P(F)-0.6 PCs l L, F)-0.8 PCSÄ°L,F)=0.3 P(AIS)-0.7 A G P(GIS)-0.8 P(AI S)-0.3 (c) What is P(S)? (d) What is P(S A)? PCGÄ°S)-0.2


ANSWER

c)
P(S) = P(S|L,F)P(L)P(F)+P(S|~L,F)P(~L)P(F)+
          P(S|L,~F)P(L)P(~F)+P(S|~L,~F)P(~L)P(~F)
       = 0.4*0.6*0.8+0.6*0.6*0.5+0.4*0.4*0.6+0.6*0.4*0.3
      =0.54
d)
P(S|A)
= P(S,A) / [P(A|S)P(S)+P(A|~S)P(~S)]
= (0.54*0.7)/(0.54*0.7+0.46*0.3)
=0.733

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