Using the information provided in the table, the network diagram and the expected project completion time $=39$ weeks:

$\backslash$table$[[$Activity$,\backslash$table$[[$Optimistic Time$],[($weeks$)]],\backslash$table$[[$Most Likely Time$],[($weeks$)]],\backslash$table$[[$Pessimistic Time$],[($weeks$)]]],[$A$,8,10,12],[$B$,4,10,16],[$C$,4,5,6],[$D$,6,8,10],[$E$,4,7,12],[$F$,6,7,9],[$G$,4,8,12],[$H$,3,3,3]]$

The critical path is A$-$B$-$D$-$G$-$H$.$

$($Round your answers to $4$ decimal places, e$.$g$.1\mathrm{.}7582.)$

$($a$)$ Calculate the probability of completing the project in $37$ weeks.

project $37$

$($b$)$ Calculate the probability of completing the project in $42$ weeks.

project $42$