Given a Bayesian network as shown below,

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

BlackTom AI · Accepted Answer

To tackle this problem, I will lay out the key facts and then walk through the calculations step by step.

First, restate the essential probabilities from the Bayes network:
- Prior probability of a burglary: P(B) = 0.001
- Prior probability of an earthquake: P(E) = 0.002
- The alarm A depends on B and E with the following conditional probabilities P(A = true | B, E): tt = 0.95, tf = 0.94, ft = 0.29, ff = 0.001, where the first letter indicates B and the second indicates E.
- The JohnCalls node J depends on A with P(J = true | A) = 0.90 and P(J = true | not A) = 0.05. Consequently, P(J = false | A) = 0.10 and P(J = false | not A) = 0.95.

Now evaluate the two blanks in turn.

1) Probability of the event in which John did not call, given the alarm does not sound (i.e., P(J = false | not A)).
- The value of J depends only on A, not directly on B or E. Therefore, once we condition on not A, J’s behavior is determined by the probabilities conditional on not A.
- Specifically, P(J = false | not A) = 1 − P(J = true | not A) = 1 − 0.05 = 0.95.
- This result is independent of how the alarm outcome not A arises from B and E in the network.
- Hence the first blank is 0.950.

2) Probability of having an earthquake (i.e., P(E)).
- From the network, the prior probability of an earthquake is given directly as P(E) = 0.002.
- There is no conditioning on other variables for this marginal probability in the question, so we simply report the prior.
- Hence the second blank is 0.002.

Putting it together, the filled-in values are 0.950 for the first blank and 0.002 for the second blank, each kept to three decimal places as requested.

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 John did not call, given the alarm does not sound, is [Fill in the blank] and the probability of having an earthquake is [Fill in the blank] (keep three decimal places).

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