Consider the Bayesian network represented by the directed acyclic graph given below:
We are given the following probabilities:
- P(tampering) = 0.02
- P(fire) = 0.01
- P(alarm | fire ∧tampering) = 0.5
- P(alarm | fire ∧¬tampering) = 0.99
- P(alarm | ¬fire ∧tampering) = 0.85
- P(alarm | ¬fire ∧¬tampering) = 0.0001
- P(smoke | fire ) = 0.9
- P(smoke | ¬fire ) = 0.01
- P(leaving | alarm) = 0.88
- P(leaving | ¬alarm ) = 0.001
- P(report | leaving ) = 0.75
- P(report | ¬leaving ) = 0.01
How do I calculate the probability of P(smoke = T | report = T )?
Context: This problem is from the following page: http://artint.info/html/ArtInt_148.html
- P(A|B) = probability of A given B
- P(A|B∧C) = probability of A given (B and C)
- P(A|¬D) = probability of A given (not D)
- A = T = A is True, i.e. the event A occurs
I am still confused by the formulae, even though I know the basic formula for Bayes' Theorem. When it comes to joint probability function it still seems confusing and I could use some of explanation to make it clear. Thank you very much in advance for your time and help.