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 of a cavity, given evidence of a toothache, P(cavity | toothache) is __________.
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Correct answer: B. 0.600
Explanation
P(toothache) = 0.108 + 0.012 + 0.016 + 0.064 = 0.2 and P(cavity ∧ toothache) = 0.12, so P(cavity | toothache) = 0.12/0.2 = 0.6.
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