A smell of sulphur (S) can be caused either by rotten eggs (E) or as a sign of the doom brought by the Mayan Apocalypse (M). The Mayan Apocalypse also causes the oceans to boil (B). The Bayesian network and corresponding conditional probability tables for this situation are shown in Figure S13.28. 

a. Compute the joint probability P(−e, −s, −m, −b). 

b. What is the probability that the oceans boil? 

c. What is the probability that the Mayan Apocalypse is occurring, given that the oceans are boiling? 

d. What is the probability that the Mayan Apocalypse is occurring, given that there is a smell of sulphur, the oceans are boiling, and there are rotten eggs? 

e. What is the probability that rotten eggs are present, given that the Mayan Apocalypse is occurring?

Figure S13.28

Transcribed Image Text:

P(E) +e 0.4 -e 0.6 P(S|E, M) +e+m+s 1.0 +e+m-8 0.0 +e-m +8 0.8 +e-m-8 0.2 -e+m+s 0.3 -e+m-s 0.7 -e-m+s 0.1 -e-m-s 0.9 E S M B P(M) +m 0.1 -m 0.9 P(B|M) +m+b 1.0 +m-b0.0 -m+b0.1 -m-b0.9