Consider the following Bayes Net over five boolean-valued random variables. a) [

Question

Consider the following Bayes Net over five boolean-valued random variables.

a) [6] What is the probability of thunder?
b) [6] What is the probability of thunder given a forest fire?
c) [6] What is the probability that there is a storm given that there is thunder? d) [6] What is the probability of camp fire given that there is no thunder?

e) [6] What is the probability of a lightning and a forest fire?

Consider the following Bayes Net over five boolean-valued random variables. a) [6] What is the probability of thunder? b) [6] What is the probability of thunder given a forest fire? c) [6] What is the probability that there is a storm given that there is thunder? d) [6] What is the probability of camp fire given that there is no thunder? e) [6] What is the probability of a lightning and a forest fire?

Explanation / Answer

a)
P(Thunder) = P(Storm=T)*P(Lightning=T|Storm)*P(Thunder=T|Lightning)
   = 0.2*0.7*0.94 = 0.1316

b)

If Forest fire then P(Thunder) = P(Lightning=F|Storm)*P(Thunder=T|Lightning=F)
           = 0.3*0.25 = 0.075

c)

P(Storm|Thunder=T) = 0.94*0.25*0.7 = 0.1645

e)

P(Lightning|Forest Fire) = 0.6*0.5 =0.3

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