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).
![1132_figure.png](https://secure.tutorsglobe.com/CMSImages/1132_figure.png)
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?