Next five questions are based on the following passage. Consider a domain…
2021
Next five questions are based on the following passage. Consider a domain consisting of three Boolean variables Toothache, Cavity, and Catch. The full joint distribution is a 2×2×2 table as shown in the figure below.
The marginal probability of cavity P(cavity) is __________.
- A.
0.200
- B.
0.216
- C.
0.120
- D.
0.080
Attempted by 41 students.
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Correct answer: A
Key idea: the marginal probability of cavity is the sum of all joint probabilities where cavity = true.
Identify the joint entries with cavity = true:
toothache = true, catch = true: 0.108
toothache = true, catch = false: 0.012
toothache = false, catch = true: 0.072
toothache = false, catch = false: 0.008
Sum these probabilities:
0.108 + 0.012 + 0.072 + 0.008 = 0.200
Therefore, the marginal probability P(cavity) = 0.200.