Given:

$\backslash$table$[[$Activity$,$Optimistic,Most Likely,Pessimistic$],[$A$,3,4,5],[$B$,6,7,14],[$C$,6,9,12],[$D$,0\mathrm{.}5,1,1\mathrm{.}5],[$E$,2,3,10],[$F$,4,5,12],[$G$,1,3,11]]$

Determine:

$($a$)$ the critical path.

$($b$)$ the probability that the project will be completed in $22$ weeks.