Given a Bayesian network as shown below,

Fill in the following blanks.

The probability of the alarm sounding when there is an earthquake but no a burglary is [blank1] (keep three decimal places).

Question

Given a Bayesian network as shown below,

Fill in the following blanks.

The probability of the alarm sounding when there is an earthquake but no a burglary is [blank1] (keep three decimal places).

BlackTom AI · Accepted Answer

Start by identifying the given conditions: there is an earthquake (E = true) and there is no burglary (B = false). In this Bayesian network, the Alarm node A has a conditional probability table P(A | B, E).

Next, locate the row in the CPT corresponding to B = false (f) and E = true (t). The CPT entry for that combination is P(A = true | B = f, E = t) = 0.29.

Since the question asks for the probability that the alarm sounds (A = true) under these exact conditions, you simply read off the value from the table: 0.29.

Expressed to three decimal places, this is 0.290.

Why other potential interpretations are not correct here:
- If Burglary were true (B = t) and Earthquake true (E = t), the CPT would give P(A = true | B = t, E = t) = 0.95, which is not the scenario described.
- If Earthquake were false (E = f) with any burglary status, the corresponding CPT entries (e.g., B = f, E = f gives 0.001; B = t, E = f gives 0.94) do not match the given condition of E = true and B = false.

Thus, under E = true and B = false, the probability the alarm sounds is 0.290.

42172 Introduction to Artificial Intelligence - Spring 2025 Lec11 class quiz

Given a Bayesian network as shown below, Fill in the following blanks. The probability of the alarm sounding when there is an earthquake but no a burglary is [blank1] (keep three decimal places).

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