A Persian rug importer receives a large shipment of 7' by 12' rugs. A sampling of the rugs receives revealed the shipment contain too many imperfections to sell at full price. Specifically, it has been determined that the number of imperfections per rug follows a Poisson distribution with an average of 3.4.

A customer randomly selects a rug. What is the probability that this rug has:

Part (a) No imperfections?
(If rounding use at least four digits after the decimal in your answer)

Part (b) At least one imperfection?
(If rounding use at least four digits after the decimal in your answer)

Part (c) Think back to conditional probability, if the rug has at most three imperfections, what is the probability it will have exactly one imperfection?
(If rounding use at least four digits after the decimal in your answer)