According to the Department of Transportation, United Airlines lost an average of 2.01 bags per 1,000 passengers during October 2017. Assume the number of lost bags follows the Poisson distribution.

a. What is the probability that, of the next 1,000 United passengers, nobody will lose their bag?

b. What is the probability that, of the next 1,000 United passengers, fewer than three will lose their bag?

c. What is the probability that, of the next 500 United passengers, nobody will lose their bag?

d. What is the probability that, of the next 500 United passengers, fewer than three will lose their bag?