Q$4.(4$x$10$ points$)$ Given the full joint distribution shown in the Figure below, calculate the following:

a$.$ P$($toothache$)$

b$.$ P$($Cavity$)$

c$.$ P$($Toothache $|$ cavity$)$

d$.$ P$($Cavity $|$ toothache V catch$)$

$\backslash$table$[[,$toothache,$-$toothache$],[,$catch,$-$catch,catch,$-$catch$],[$cavity$,0\mathrm{.}108,0\mathrm{.}012,0\mathrm{.}072,0\mathrm{.}008],[$acavity$,0\mathrm{.}016,0\mathrm{.}064,0\mathrm{.}144,0\mathrm{.}576]]$

Figure. A full joint distribution for the Toothache, Cavity, Catch world.