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?

1. A<0.2,0.8>
2. B<0.4,0.8>
3. C<0.6,0.8>
4. D<0.6,0.4>

Pick an option to check yourself, or open the answer below.

Show answer & explanation

Correct answer: D. <0.6,0.4>

Explanation

P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2; P(cavity ∧ toothache) = 0.12. So P(Cavity | toothache) = ⟨0.12/0.2, 0.08/0.2⟩ = ⟨0.6, 0.4⟩.