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I'm reading through the section on Bayesian modelling (5.1.1) and following fine up to the example of Ping and Greg (!/book/machine-learning-systems/chapter-5/point-2869-44-44-0). At this point there's a couple of issues:
- P(V) is asserted to be 0.2+0.1+0.2=0.5 without justification
- the entire calculation does not match my understanding of Baye's rule (with the 'naive' assumption)

Let me write capitals (F, G, C) for the cases that the matched bears agree (on food, going out, and cubs respectively) and lower case when they disagree. So 'P(f | M)' is the probability of the pair of bears disagreeing on their favourite food given that they are a match.

So for Ping and Greg V = f, G, c (they only agree on going out). Given the instances in table 5.1 P(f, G, c) = 0.2, so
P(M | f, G, c) = P(f | M) * P(G | M) * P(c | M) * P(M) / P(f, G, c)
= 0.5 * 1 * 0 * 0.6 / 0.2
= 0

The implementation seems to be consistent with my calculation for P(V).

Am I off track here, or is there an issue with this example (and possibly with the implementation that follows)?