Fernando et al.* studied drugsharing 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 researcher 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 shown in the table below: l Gender Split Drugs (5) Never Split Drugs (N) Total | Male [M] 349 324 673 1 Female (F) 220 128 348 Total 569 452 1021 lFernando, D., Schilling, R., Fontdevila, J., and El~Bassel, Nabila (2003). Predictors of Sharing Drugs among Injection Drug Users in the South Bronx: Implications for HIV Transmission, Journal of Psychooctfve Drugs, 35, 221236. 1. How many marginal probabilities can be calculated from these data? State each in probability notation and do the calculations (i.e., what is the probability based on these data?). 2. How manyjoint probabilities can be calculated? State each in probability notation and do the calculations. 3. State the following probabilities in words and calculate the probability for each: P[F n 5) PM U M) P(5|Fl PlNIMl 4. Would splitting drugs (5) and male gender (M) be considered independent events