Given the following activity network: $(3$ activities A$1,$ A$2,$ & A$3$; arrows point from A$1$ to A$2$ & A$1$ to 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 estimate considering all scenarios?

Group of answer choices

$9$ weeks

$10$ weeks

$12$ weeks

$13\mathrm{.}5$ weeks