Graph Algorithms · Superchallenge problem

Six tasks $a,b,c,d,e,f$ have prerequisites $a$ before $b$, $a$ before $c$, $b$ before $d$, $b$ before $e$, $c$ before $f$. A valid order of all six tasks is chosen uniformly at random from all possibilities. What is the probability that task $d$ comes before task $f$?