$6-(20$ pts$)$ A rural highway has one lane in each direction. In one direction $V=300ve\frac{h}{h}\frac{r}{ln}$ at

a railroad crossing. The barriers at this crossing are lowered to block vehicles for four minutes

and $30$ seconds for a train to pass. What is the probability that when the barrier is lifted, the

queue has exactly nine vehicles? Assume no initial queue.