SOLUTION: A safety officer carried out of a survey of 100 lung cancer patients with the following results: 45 smokers who lived in urban areas, 37 of whom did not have a hazardous occupation

Question 1134469: A safety officer carried out of a survey of 100 lung cancer patients with the following results: 45 smokers who lived in urban areas, 37 of whom did not have a hazardous occupation; 20 people with hazardous occupation, of whom 10 live in urban areas and 10 smoke; 75 smokers; and 10 who neither smoke, nor have a hazardous occupation, nor live in an urban area;
(i) How many patients with hazardous occupations neither smoke nor live in urban areas?
(ii) How many patients live in an urban area?
(iii) How many patients smoke and they do not have a hazardous occupation?
(iv) How many patients smoke, have hazardous occupation and live in urban areas?
(Hint: Use Venn diagram)
Answer by Glaviolette(140) (Show Source): You can put this solution on YOUR website!
To create the venn diagram, I noted that the total needs to be 100 and we have 10 on the outside who did not fall into any of the categories. Since 45 smokers lived in urban areas, but 37 did not have a hazardous occupation, that puts the 37 in the sm and u overlap and 8 (45-37) in the area where all 3 overlap. 20 people have a haz occupation, of whom 10 live in urban. 8 of those 10 were already accounted for leaving just 2 to be in u and ho overlap. Same is true for the 10 who smoke. With a total of 20 in HO, 12 have been assigned, leaving 8 for just HO. Last to fill in was just the U. All the values were added together for 85. We need 90 in the circles, so 5 are in the U only part.
i. 8
ii. 2+8+37+5 = 52
iii. 28+37 = 65
iv. 8
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