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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 probability of a toothache, given evidence of a cavity, $P(toothache\mid cavity)$ is ________.

Solution


$P(toothache\mid cavity)=\frac{P(toothache\cap cavity)}{P(cavity)}$

From table,

$P(toothache\cap cavity)=0.108+0.012=0.120$

Also,

$P(cavity)=0.108+0.012+0.072+0.008=0.200$

So,

$P(toothache\mid cavity)=\frac{0.120}{0.200}=0.600$

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