The voftware solution division at Mastek Inc, has been working on an application which on development would buve a large market. In order to remain market leaders and innovators of new products, they have to complete this project as won as possible. The dixision ananger resorts to the use of PERT in the scheduling of the project activities. The following table depicts the information on the activities:

$\backslash$table$[[,$Duration $($Days$)],[$Activity$,\backslash$table$[[$Immediate$],[$Prodecesor$($s$)]],$Optimistic $($a$),$Most Likely $($m$),$Prssimistic $($b$)],[$A$,-,2,3,4],[$B$,$A$,2,4,6],[$C$,$A$,4,5,12],[$D$,$A$,1,3,5],[$E$,$B$,2,2,2],[$F$,$B$,3,6,9],[$G$,$C$,5,7,15],[$H$,$E$,$ G$,$ D$,4,8,12],[$I$,$D$,6,15,18],[$I$,$E$,$ F$,$ G$,$ D$,3,4,5],[,,,,]]$

$($a$)$ Find the critical path and the expected project completion time through a PERT nefuork diagram.

$($b$)$ What is the probubility that the project will be compleised within $30$ days?