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A domain is modeled by three Boolean variables Toothache, Cavity and Catch. They stand for the propositions 'the patient has a toothache'; 'the patient has

A domain is modeled by three Boolean variables Toothache, Cavity and Catch. They stand for the propositions 'the patient has a toothache'; 'the patient has a cavity'; 'the dentist catches in the patients tooth with his nasty steel probe', respectively.

The table shows the joint probabilities of the model.

Toothache

^toothache

Catch

^catch

catch

^catch

Cavity

0.108

0.012

0.072

0.008

^cavity

0.016

0.064

0.144

0.576

Consider the following statements.

(i) P(^toothache|cavity) = 0.34

(ii) The variables Toothache and Catch are conditionally independent given Cavity

= true.

Which of these statements are true

a.

only (i) is true

b.

only (ii) is true

c.

both (i) and (ii) are true

d.

both (i) and (ii) are false.

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