Directions (Q56–60): A domain has three Boolean variables Toothache, Cavity and Catch, with full joint distribution: cavity ∧ toothache: catch 0.108, ¬catch 0.012; cavity ∧ ¬toothache: catch 0.072, ¬catch 0.008; ¬cavity ∧ toothache: catch 0.016, ¬catch 0.064; ¬cavity ∧ ¬toothache: catch 0.144, ¬catch 0.576.
The probability for Cavity, given that either Toothache or Catch is true, P(Cavity | toothache ∨ catch) is _______.
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Correct answer: D. 0.4615
Explanation
P(toothache ∨ catch) = 1 − P(¬toothache ∧ ¬catch) = 1 − (0.008 + 0.576) = 0.416. P(cavity ∧ (toothache ∨ catch)) = 0.108 + 0.012 + 0.072 = 0.192. Ratio = 0.192/0.416 ≈ 0.4615.
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