4. Several hundred students were followed over the course of two years from 9\"

Question

4. Several hundred students were followed over the course of two years from 9" grade to 10t grade. They were asked each year to respond to questions regarding their substance use in the month preceding the questionnaire. The results with respect to their responses regarding alcohol consumption are tabulated below Orink 1 year Yes Orink 1 year No Totals Drink 2 year Yes 500 372 872 Drink 2nd Year No 124 565 589 Totals 624 937 1561 a) Find the marginal probability of a student reporting (Yes) that they drank in the second year. 3 points) b) Find the conditional probability that a student reported drinking in the first year given that they reported drinking in the second year. (3 points) Find the conditional probability that a student reports drinking in the second year, given that they reported drinking in the first. (3 points) d) Use a logical argument to explain whether drinking in the second year can be considered independent of drinking in the first year. [3 points) e) What is the probability of drinking in both the first and second year? What is the probability of not drinking in both years? (6 points)

Explanation / Answer

a)P(marginal probability of drinking in second year)=872/1561=0.5586

b)

P(drink first year|drink 2nd year)=500/872=0.5734

c)P(drink second year|drink 1st year) =500/624=0.8013

d)

as drinking is chronic and person who is drinking in 1st year is inclined to drink in 2nd year ; therefore they are depedent

e)

P(drinking in both first and second year)=500/1561=0.3203

P(not drinking in both years) =1-0.3203 =0.6797

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