Given the following activity network: Three nodes $-$ A$1,$ A$2,$ A$3$; two paths $-$ A$1,$ A$2$ and A$1,$ A$3.$

Activity A$1$ takes $5$ weeks, A$2$ takes $7$ weeks, and A$3$ takes $4$ weeks with a $50\%$ probability and $10$ weeks with a $50\%$ probability. What is the project completion time under the worst$-$case scenario, that is$,$ A$3$ is late and takes $10$ weeks?

Question $7$ options:

A$)$

$10$

B$)$

$15$

C$)$

$9$

D$)$

$12$