The following table lists the activity time estimates $($in weeks$)$ for each activity.

$\backslash$table$[[$Activity$,$Optimistic,Most Probable,Pessimistic$],[$A$,4,5,6],[$B$,2\mathrm{.}5,3,3\mathrm{.}5],[$C$,5,6,7],[$D$,5,5\mathrm{.}5,9],[$E$,5,7,9],[$F$,2,3,4],[$G$,7,9,11],[$H$,7,8,15]]$

Based only on the critical path, what is the estimated probability that the project will be completed within the given time frame? $($Round your answers to four

$($a$)$ Within $21$ weeks?

$($b$)$ Within $23$ weeks?

$($c$)$ Within $27$ weeks?