Question: A wire manufacturing company has inspectors to examine the wire for fractures as it comes out of a machine. The number of fractures is distributed in accordance with a Poisson process, having one fracture on the average for every 60 meters of wire. One day an inspector had to take an emergency phone call, so she left her post for a few minutes. Later on, she was informed that, while she was away from her post, 200 meters of wire was manufactured with three fractures. What is the probability that the consecutive fractures, among this portion of wire manufactured, were at least 60 meters apart? Hint: Let N (t) be the number of fractures in the first t meters of wire manufactured after the inspector left her post; $ N (t): t ≥ 0 % is a Poisson process with rate 60.