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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
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.
The probability for Cavity, given that either Toothache or Catch is true, $P(Cavity\mid toothache\vee catch)$ is ________.
| toothache | $\neg$toothache | |||
|---|---|---|---|---|
| catch | $\neg$catch | catch | $\neg$catch | |
| cavity | $0.108$ | $0.012$ | $0.072$ | $0.008$ |
| $\neg$cavity | $0.016$ | $0.064$ | $0.144$ | $0.576$ |
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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