Thanks for helping me with this problem! Kwebwork / f2017stat213102/21317 assign

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Kwebwork / f2017stat213102/21317 assignment 2/1 213F17 Assignment 2: Problem 1 Previous Problem Problem List Next Problem (1 point) The Canadian Tobacco Monitoring Survey is a national survey administered by Statistics Canada to study smoking trends of Canadians aged 15 or older. The most recent survey found that 20% of Canadians aged 15 years or older smoke on a daily basis. In addition, 21% of men are smokers, and 19% of women are smokers. The most recent census shows that men make up 50% of the Canadian population, with women making up the remainder You randomly pick a Canadian that is 15 years old or older. What is the probability this person Part (a) is male and a smoker? | (Use four decimals in your answer) (Use four decimals) Part (b) is a women and not a smoker? Part (c) What percentage of smokers are male? Part (d) What percentage of smokers are women? % %(enter your percentage to two decimals) 111 % (enter your percentage to two decimals)

Explanation / Answer

P(smokers) = 0.20

P(smokers|Men) = 0.21

P(Smokers|Women) = 0.19

P(Men) + P(Women) = 1

And from Bayes theorem we get

P(Men)*P(Smokers|Men) + P(women)*P(Smokers|Women) = P(Smokers)

P(Men)*0.21+(1-P(Men))*0.19 = 0.20

0.02*P(Men)+0.19 = 0.20

P(Men) = 0.01/0.02 = 0.5

a)

P(Men and Smoker) = P(Smoker|Men)*P(men) = 0.21*0.5 = 0.105

b)

P(Women and Not aSmoker) = P(women) - P(Women and Smoker) = 0.5 - 0.19*0.5 = 0.405

c)

P(Men|Smokers) = P(Men and Smokers) /P(Smokers) = 0.105/0.20 = 0.525

d)

P(Women|Smokers) = P(Women and Somkers)/P(Smokers) = 0.095/0.20 = 0.475

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