$($Chapter $19$ Project Management$)$ A project consists of $4$ activities: A$,$ B$,$ C and D$.$A is known to take $5$ days, while B takes $5$ days $50\%$ of the time and $8$ days $50\%$ of the time. Project C takes $4$ days all the time. Project D takes $2$ days half of the time. But, the other half of the time, it is delayed and takes $7$ days. The project network with dependencies is shown below. Each scenario is equally likely to occur.