Draw a PERT network diagram for a construction project with the activity information given below.

a$)$ Identify the critical path.

b$)$ Determine the probability of completing the project in two years $(104$ weeks$)$

Please answer all parts of the question and draw a diagram $\backslash$begin$\{$tabular$\}\{|$c$|$c$|$c$|$c$|$c$|\}$

$\backslash$cline $\{3-5\}\backslash$multicolumn$\{2\}\{$c$|\}\{\}$ & $\backslash$multicolumn$\{3\}\{$c$|\}\{$ Duration $($Weeks$)\}\backslash \backslash$

$\backslash$hline Activity & $\backslash$begin$\{$tabular$\}\{$c$\}$

Immediate $\backslash \backslash$

Predecessor$($s$)$

$\backslash$end$\{$tabular$\}$ & Optimistic $(\backslash ($ a $\backslash ))$ & Most Likely $($m$)$ & Pessimistic $($b$)\backslash \backslash$

$\backslash$hline A & $-$ & $7$ & $16$ & $28\backslash \backslash$

$\backslash$hline B & A & $4$ & $19$ & $25\backslash \backslash$

$\backslash$hline C & A & $10$ & $16$ & $37\backslash \backslash$

$\backslash$hline D & B & $7$ & $13$ & $37\backslash \backslash$

$\backslash$hline E & B$,$ C & $13$ & $19$ & $33\backslash \backslash$

$\backslash$hline F & B & $19$ & $22$ & $33\backslash \backslash$

$\backslash$hline G & D$,$ E & $4$ & $7$ & $19\backslash \backslash$

$\backslash$hline H & F$,$ G & $13$ & $19$ & $37\backslash \backslash$

$\backslash$hline I & B$,$ C & $13$ & $25$ & $19\backslash \backslash$

$\backslash$hline J & I, H & $7$ & $13$ & $\backslash \backslash$

$\backslash$hline

$\backslash$end$\{$tabular$\}$