Given a Bayesian network as shown below,

Fill in the following blanks.
The probability of the event in which Mary did not call, given the alarm does not sound, is [Fill in the blank]
and the probability of having a Burglary is [Fill in the blank]
(keep three decimal places).

Question

Given a Bayesian network as shown below,

Fill in the following blanks.
The probability of the event in which Mary did not call, given the alarm does not sound, is [Fill in the blank]
 and the probability of having a Burglary is [Fill in the blank]
 (keep three decimal places).

BlackTom AI · Accepted Answer

To approach the blanks, I’ll break down the computations using the given Bayesian network and CPTs, and then connect them to the requested probabilities.

First, restate what we need:
- Probability Mary did not call given the alarm does not sound: P(M=false | A=false).
- Probability of having a Burglary: P(B=true).

Now evaluate P(M=false | A=false):
- MaryCalls depends on A via the CPT P(M=true | A).
  • If A = true, P(M=true | A=true) = 0.70, so P(M=false | A=true) = 0.30.
  • If A = false, P(M=true | A=false) = 0.01, so P(M=false | A=false) = 0.99.
- The question asks for P(M=false | A=false). Therefore, once we condition on A=false, the probability Henry did not call simplifies to 0.99 directly, since M is conditioned on A and there is no additional dependence on B or E given A.

Thus, P(M=false | A=false) = 0.99, which matches the first fill-in value of 0.990 (to three decimals).

Next, evaluate P(B):
- The prior probability of a burglary is given in the network as P(B) = 0.001.
- This is unconditional; no other evidence is specified to alter it here, so P(B=true) = 0.001.

Therefore, P(B=true) = 0.001, which is the second fill-in value to three decimals.

Summary of the key reasoning steps:
- Recognize that M’s probability given A is specified, so conditioning on A=false yields P(M=false | A=false) = 0.99 directly from the provided CPT.
- The burglary probability is the network prior P(B) = 0.001, independent of Mary’s or alarm states unless further evidence is introduced.

These results correspond to the requested blanks: 0.990 for the Mary-not-calling given no alarm, and 0.001 for the burglary probability.

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 event in which Mary did not call, given the alarm does not sound, is [Fill in the blank] and the probability of having a Burglary is [Fill in the blank] (keep three decimal places).

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