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 3.4.2 LEE CLARK 3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative 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: 66 Never Split Drugs Gender Split Drugs Total MOITIMINg 324 673 349 Male 128 348 Female 220 452 1021 Total 569 gen selet A 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 nota- tion 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?

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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
3.4.2
Transcribed Image Text: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 3.4.2
LEE CLARK
3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative
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:
66
Never Split Drugs
Gender
Split Drugs
Total
MOITIMINg
324
673
349
Male
128
348
Female
220
452
1021
Total
569
gen selet A
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 nota-
tion 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?
Transcribed Image Text:LEE CLARK 3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative 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: 66 Never Split Drugs Gender Split Drugs Total MOITIMINg 324 673 349 Male 128 348 Female 220 452 1021 Total 569 gen selet A 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 nota- tion 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?
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