Question No: $04$

$\backslash$table$[[$Activity$,$Predecessor,Optimistic time,Most Likely Time,Pessimistic Time$],[$A$,-,2,4,6],[$B$,-,2,2,3],[$C$,-,4,8,10],[$D$,$A$,4,6,7],[$E$,$A$,$ B$,7,9,12],[$F$,$D$,$ E$,1,2,3],[$G$,$C$,2,3,4]]$

$($a$)$ Draw the project network, find the expected durations for each activity, the expected project duration and the critical path.

$($b$)$ Find the total slack and free slack for non$-$critical activities.

$($c$)$ Find the probability that the project will be completed

$($i$)$ at least $3$ days earlier than expected project duration?

$($ii$)$ at most $3$ days after the expected project duration?