The product development group at Electronica Telecom has been working on a new software product that has the potential to capture a large segment of the market. Through external sources, Telecom's management became aware that the competitor is working on a similar product. Consequently, Telecom's top management increased its pressure on the product development group. The group leader resorted to the PERT$/$CPM procedure to schedule the remaining activities before the new product can be brought to market.

$\backslash$table$[[,$Time in weeks$],[$Activity$,$Predecessor,Optimistic $($a$),$Most likely $($m$),$Pessimistic $($b$)],[$A$,-,4,8,12],[$B$,$A$,6,7,8],[$C$,$A$,6,12,18],[$D$,$A$,3,5,7],[$E$,$C$,$D$,6,9,18],[$F$,$B$,$C$,5,8,17],[$G$,$E$,$F$,10,15,20],[$H$,$F$,$G$,5,6,13]]$

a$)$ Develop a network diagram and identify the critical path activities and duration time.

b$)$ What is the probability that the project will be completed so that Electronica Telecom can launch the new product within $25$ weeks? Within $30$ weeks?