Inference By Enumeration

Consider the following Bayesian network. C, F, B and S are boolean variables. Assume you perceive a burnt smell (S=true). You know that this is typically caused either by a fire (F) or by burnt food (B). You also know that either the fire or the burnt food may be caused by your friend cooking (C).

The prior probability for cooking is P(c) = 0.6.

Here are the conditional probability distributions:

P(F = true | C=true) = 0.2

P(F = true | C=false) = 0.1

P(B = true | C=true) = 0.5

P(B = true | C=false) = 0.0

P(S = true | F = true, B=true) = 0.9

P(S = true | F = true, B=false) = 0.6

P(S = true | F = false, B=true) = 0.5

P(S = true | F = false, B=false) = 0.1

Write down the joint probability distribution for C, F, and B (you already know that S=true). Then answer the following questions and show your computation:

a) What is the probability that your friend is cooking given that you perceive a burnt smell?

b) What is the probability that the house is on fire given that you perceive a burnt smell?