3.4.2 Fernando et al. (A-3) studied drug-sharing among injection drug users in the South Bronx in New York City. Drug users in New York City use the term "split a bag" or "get down on a bag" to refer to the practice of dividing a bag of heroin or other injectable substances. A common practice includes splitting drugs after they are dissolved in a common cooker, a procedure with considerable HIV risk. Although this practice is common, little is known about the prevalence of such practices. The researchers asked injection drug users in four neighborhoods in the South Bronx if they ever "got down on" drugs in bags or shots. The results classified by gender and splitting practice are given below: Gender Split Drugs Never Split Drugs Total Male 349 324 673 Female 220 128 348 Total 569 452 1021 Source: Daniel Fernando, Robert F. Schilling, Jorge Fontdevila, and Nabila El-Bassel, "Predictors of Sharing Drugs among Injection Drug Users in the South Bronx: Implications for HIV Transmission," Journal of Psychoactive Drugs, 35 (2003), 227-236. (a) How many marginal probabilities can be calculated from these data? State each in probability notation and do the calculations. (b) How many joint probabilities can be calculated? State each in probability notation and do the calculations. (c) How many conditional probabilities can be calculated? State each in probability notation and do the calculations. (d) Use the multiplication rule to find the probability that a person picked at random never split drugs and is female. (e) What do we call the probability calculated in part d? (f) Use the multiplication rule to find the probability that a person picked at random is male, given that he admits to splitting drugs. (g) What do we call the probability calculated in part f? 3.4.3 Refer to the data in Exercise 3.4.2. State the following probabilities in words and calculate: (a) P(Male n Split Drugs) (b) P(Male U Split Drugs) (c) P(Male | Split Drugs) (d) P(Male)