The following information relates to a project$($task times are in$$ weeks$).$ Use the information to solve for the critical path and then to determine the probability that the project could be completed within $28$ weeks.

$$

Task

Preceding Tasks

t Subscript o

t Subscript m

t Subscript p

A

None

$2$

$4$

$6$

B

A

$4$

$5$

$6$

C

A

$1$

$5$

$9$

D

B

$8$

$13$

$18$

E

C

$3$

$8$

$13$

F

$$D$,$ E

$3$

$5$

$7$

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Part $2$

The probability that the project is completed within $28$ weeks is

$$

enter your response here. $($Enter your response rounded to four decimal places.$)$