Laffy Taffy is a type of taffy candy made from corn syrup, sugar, palm oil, and other ingredients. Laffy Taffy comes in a variety of flavors including strawberry, banana, and cherry. Suppose that Laffy Taffy is produced as a continuous length of taffy on an extrusion machine. Defects can occur in the taffy including large air bubbles and tears. Assume that the distance between such defects follows an exponential distribution with a mean of 523 meters.

a. What is the probability that the machine will produce more than 1,000 meters of taffy before the next defect is observed?

b. What is the probability that the next defect will be observed before the machine produces 500 meters or less of taffy?