Chapter 3, Problem 3.123ACI

Profile of a sustainable farmer. Sustainable development or sustainable farming means finding ways to live and work the Earth without jeopardizing the future. Studies were conducted in five Midwestern states to develop a profile of a sustainable farmer. The results revealed that farmers can be classified along a sustainability scale, depending on whether they are likely (L) or unlikely (U) to engage in the following practices: (1) raise a broad mix of crops; (2) raise livestock; (3) use chemicals sparingly; and (4) use techniques for regenerating the soil, such as crop rotation.

1. a. List the different sets of classifications that are possible for the four practices (e.g., LUUL).
2. b. Suppose you are planning to interview farmers across the country to determine the frequency with which they fall into the classification sets you listed for part a. Because no information is yet available, assume initially that there is an equal chance of a farmer falling into any single classification set. Using that assumption, what is the probability that a farmer will be classified as unlikely on all four criteria (i.e., classified as a nonsustainable farmer)?
3. c. Using the same assumption as in part b, what is the probability that a farmer will be classified as likely on at least three of the criteria (i.e., classified as a near-sustainable farmer)?