3. Des Jarlais et al. (A-5) examined the failure to maintain AIDS risk reduction in a study of intravenous drug users from New York City. The following table shows the study subjects cross-classified according to risk reduction status and number of sexual partners in an average month:

Number of Sexual Partners / Month Risk Reduction Status None Not Maintained Maintained Total None 1

> 1 20 37 20 17 45 54 43 95 67 80 177 141 Total 77 116 205 398 SOURCE: Reprinted from Don C. Des Jarlais, Abu Abdul-Quader, and Susan Tross, "The Next Problem: Maintenance of AIDS Risk Reduction Among Intravenous Drug Users," The International Journal of the Addictions, 26 (1991), 1279-1292, by courtesy of Marcel Dekker, Inc.

a. We select a subject at random. What is the probability that he/she did not initiate any risk reduction?

b. We select a subject at random and find that he/she had more than one sexual partner. What is the probability that he/she maintained risk reduction?

c. We select a subject at random. What is the probability that he/she had no sexual partners and did not maintain risk reduction?

d. We select a subject at random. What is the probability that he/she had one sexual partner or initiated no risk reduction?