Public Citizen's Health Research Group studied the serious disciplinary actions that were taken during a recent year on nonfederal medical doctors in the U.S. The American average was 3.05 serious actions per 1,000 doctors. Assume that the Canadian average is the same; moreover, assume that the numbers of serious actions per 1,000 doctors is Poisson distributed.

a. What is the probability of randomly selecting 1,000 Canadian doctors and finding one serious action taken?

b. What is the probability of randomly selecting 2,000 Canadian doctors and finding four serious actions taken?