A roll of plastic-coated wire has the average of 0.09 flaws per 5-meter length of wire. Assume a quality control engineer will sample a 5-meter length of wire from the roll of wire 230 meters in length. If no flaws are found in the sample, the engineer will believe the entire roll of wire.
Given that no flaws were found in the sample, what is the probability that the complete roll has no flaws?