Refer to the USDA report on slaughtered chickens that pass inspection with fecal contamination, Exercise 3.8. Consider a sample of five chickens that have all passed the standard USDA inspection. Each chicken carcass will be classified as either passing inspection with fecal contamination or passing inspection without fecal contamination.

a. List the simple events for the sample.
b. Assuming the simple events, part a, are equally likely, find the probability that at least one of the five chickens passes inspection with fecal contamination.
c. Explain why the assumption of part a is unreasonable for this sample.

Data from Exercise 3.8

The United States Department of Agriculture (USDA) reports that, under its standard inspection system, one in every 100 slaughtered chickens passes inspection with fecal contamination.