To help with preparations, a couple has devised a project network to describe the activities that must be completed by their wedding date.

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$,5,6,13]]$

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 decimal places.$)$

$($a$)$ Within $19$ weeks?

$($b$)$ Within $21$ weeks?

$($c$)$ Within $25$ weeks?