SOLUTION: Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 97

Question 405672: Suppose that in a senior college class of 500 students it is found that 210 smoke, 258 drink alcoholic beverages, 216 eat between meals, 122 smoke and drink alcoholic beverages, 97 smoke and eat between meals, and 52 engage in all 3 of these bad health practices. If a member of this senior class is selected at random, find the probability that the student:
eats between meals but does not drink alcoholic beverages nor smokes.
Answer by tallgirl84(3) (Show Source): You can put this solution on YOUR website!
11.4% chance that the student eats between meals but does not smoke or drink.
I used a venn diagram to solve. Interlock three circles representing Smokers, Drinkers, and Eaters. In the very center would be 52. S&E is 97-52=45. D&S is 122-52=70. S is 210-70-52-45=140. Now take the 216 for E-45-52=119. Now the 258 for D-52-70=136. 136+119=255. Then take the original 500-140-70-45-52=193. So 255-193=62 for DE. D's 258-70-52-62=74. E's 216-62-52-45=57.
SO! That would leave:
Drinkers - 74
Smokers - 140
Eaters - 57
Drinkers & Smokers - 70
Smokers & Eaters - 45
Eaters & Drinkers - 62
Drinkers, Smokers, & Eaters - 52
74+140+57+70+45+62+52=500
Eaters 57 is 11.4% of 500.
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