Given a Bayesian network as shown below,

Fill in the following blank.

The probability of the event in which there is no alarm sound when there is a Burglary but no earthquake is [blank1] (keep three decimal places).

Question

Given a Bayesian network as shown below,

Fill in the following blank.

The probability of the event in which there is no alarm sound when there is a Burglary but no earthquake is [blank1] (keep three decimal places).

BlackTom AI · Accepted Answer

First, identify the given condition: there is Burglary (B = true) and there is no Earthquake (E = false). The question asks for the probability that there is no alarm sound (A = false) under these conditions.

Next, locate the conditional probability for A given B and E from the network's CPT (the table for P(A = true | B, E)). The table shows:
- P(A = true | B = true, E = true) = 0.95
- P(A = true | B = true, E = false) = 0.94
- P(A = true | B = false, E = true) = 0.29
- P(A = true | B = false, E = false) = 0.001

Since we have B = true and E = false, we use P(A = true | B = true, E = false) = 0.94.

The probability of no alarm (A = false) under these same conditions is the complement of A = true: P(A = false | B = true, E = false) = 1 − P(A = true | B = true, E = false) = 1 − 0.94 = 0.06.

Finally, round to three decimal places as requested: 0.060.

42172 Introduction to Artificial Intelligence - Spring 2025 Lec11 class quiz

Given a Bayesian network as shown below, Fill in the following blank. The probability of the event in which there is no alarm sound when there is a Burglary but no earthquake is [blank1] (keep three decimal places).

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