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UGC NET Computer Science Nov 2021 (Paper II)

Consider a domain consisting of three Boolean variables Toothache, Cavity, and Catch. The full joint distribution is a $2\times2\times2$ table as shown below.
toothache$\neg$toothache
catch$\neg$catchcatch$\neg$catch
cavity$0.108$$0.012$$0.072$$0.008$
$\neg$cavity$0.016$$0.064$$0.144$$0.576$
The marginal probability of cavity $P(cavity)$ is __________.

Solution

Marginal probability means we add all probabilities where $cavity$ is true.

From the table, cavity row values are:

$0.108,\ 0.012,\ 0.072,\ 0.008$

So,

$P(cavity)=0.108+0.012+0.072+0.008$

$P(cavity)=0.200$

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