Aspire Faculty ID #18870 · Topic: UGC NET Computer Science Nov 2021 (Paper II) · Just now
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 for Cavity, given that either Toothache or Catch is true, $P(Cavity\mid toothache\vee catch)$ is ________.

Solution

We need:

$P(Cavity\mid toothache\vee catch)=\frac{P(Cavity\cap(toothache\vee catch))}{P(toothache\vee catch)}$

Numerator:

$P(Cavity\cap(toothache\vee catch))=0.108+0.012+0.072=0.192$

Denominator:

$P(toothache\vee catch)=1-P(\neg toothache\cap \neg catch)$

$=1-(0.008+0.576)=0.416$

So,

$P(Cavity\mid toothache\vee catch)=\frac{0.192}{0.416}=0.4615$

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