A project network has two paths $($path $1$: ABDF and path $2$: CEF$)$ running through it$.$ The first path has an expected length of $15$ days and a variance of $4$ days. The second path has an expected length of $12$ days and a variance of $16$ days. What is the probability that this project can be completed in $16$ days? $($Calculate down to four decimal places$)$