A full joint distribution for the Toothache, Cavity and Catch is given in the…
2018
A full joint distribution for the Toothache, Cavity and Catch is given in the table below
What is the probability of Cavity, given evidence of Toothache?
- A.
⟨0.2,0.8⟩
- B.
⟨0.4,0.8⟩
- C.
⟨0.6,0.8⟩
- D.
⟨0.6,0.4⟩
Attempted by 25 students.
Show answer & explanation
Correct answer: D
Compute P(Cavity | Toothache) = P(Cavity and Toothache) / P(Toothache).
P(Cavity and Toothache) = 0.108 + 0.012 = 0.12.
P(Toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.20.
Therefore P(Cavity | Toothache) = 0.12 / 0.20 = 0.6.
So the posterior distribution over Cavity given Toothache is ⟨0.6, 0.4⟩ (Cavity = true, Cavity = false).