P$4.(10$ points$)$ A project consists of activities listed in the following table.

Activity Immediate

predecessor

Optimistic

Time$($Days$)$

Mostly likely

Time$($Days$)$

Pessimistic

Time$($Days$)$

A $-567$

B $-6813$

C $-81318$

D A $111420$

E B $345$

F C $7914$

G E $4710$

End D$,$F$,$G

a$)$ Please indicate the critical path, based on the expected activity duration $($forward and

backward pass analysis is not required$).$

b$)$ Suppose the project will get a reward, if it is completed within $21$ days. What is the

probability of getting the reward?