Question

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 20.25% of Canadians aged 15 years or older smoke on a daily basis. In addition, 24% of men are smokers, and 16.5% 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)

Part (b) is a women and not a smoker?

(Use four decimals)

Part (c) What percentage of smokers are male?

%(enter your percentage to two decimals)

Part (d) What percentage of smokers are women? %

% (enter your percentage to two decimals)

Answer 1

Let us create a 2x2 table Contigency table

Given 50% are men and remaining(100-50) i.e 50% are women

therefore,

	Male	Female	Total
Smoker
Non Smoker
Total	50	50	100

The most recent survey found that 20.25% of Canadians aged 15 years or older smoke on a daily basis

Therefore

	Male	Female	Total
Smoker			20.25
Non Smoker			100-20.25 = 79.75
Total	50	50	100

Also given,

24% of men are smokers, and 16.5% of women are smokers. Therefore 24% of 50 men = 12 and 16.5% of 50 women = 8.25

	Male	Female	Total
Smoker	12	8.25	20.25
Non Smoker	50-12=38	50-8.25=31.75	100-20.25 = 79.75
Total	50	50	100

Finally,

	Male	Female	Total
Smoker	12	8.25	20.25
Non Smoker	38	31.75	79.75
Total	50	50	100

Part (a) probability this person is male and a smoker

probability this person is male and a smoker= Total number of persons who are male and smoker / Total number persons = 12/100 = 0.12

probability this person is male and a smoker = 0.12

Part (b) Probability that this person is a women and not a smoker

Probability that this person is a women and not a smoker = Total number of persons who are Female and non- smoker / Total number persons = 31.75/100 = 0.3175

Probability that this person is a women and not a smoker = 0.3175

Part (c) What percentage of smokers are male?

percentage of smokers are male = (Total persons who are smokers and male / Total number of smokers ) *100 = (12/20.25)*100 = 59.2593%

percentage of smokers are male = 59.2593%

Part (d) What percentage of smokers are women? %

percentage of smokers are women =  (Total persons who are smokers and women / Total number of smokers ) *100 = (8.25/20.25)*100 = 40.7407%

percentage of smokers are women =  40.7407%