Problem $1$

Consider the following project table:

$\backslash$table$[[$Activity$,\backslash$table$[[$Immediate$],[$Predecessors$]],$m $($weeks$),$a $($weeks$),$b $($weeks$)],[$A$,-,5,2,8],[$B$,-,5,1,9],[$C$,$A$,6,4,9],[$D$,$B$,2,2,2],[$E$,$A$,2,1,9],[$F$,$C$,$ D$,4,2,5],[$G$,$C$,$ E$,8,3,10],[$H$,$F$,$ G$,2,1,3]]$

What is the probability that the project can be completed in $19$ weeks? Please provide an explanation for your answer.