Suppose that in a senior college class of 500 students, it is found that 194 smo

Question

Suppose that in a senior college class of 500 students, it is found that 194 smoke, 224 drink alcoholic beverages, 201 eat between meals, 104 smoke and drink If a member of this senior class is selected at random, find the prob and drinks alcoholic beverages but does not smoke, (c) neither smokes nor eats between meals holic beverages, 61 eat between meals and drink alcoholic beverages, 82 smoke and eat between meals, and 33 engage in all three of these bad health practices bility that the student (a) smokes but does not drink alcoholic beverages, (b) eats between meals

Explanation / Answer

let number who smoke =A ; drink =B and eat between meals =C

also as AUB =A+B-AnB

hence

a)number who smoke but does not drink =N(A)-N(AnB) =194-104=90

hence probability =90/500=0.18

b)number who eat betwen meal and drink but does not smoke =N(BnC)-N(AnBnC) =61-33=28

hence probability =28/500=0.056

c)

number who neither smoke nor eat between meals =500-N(AUC)=500-313=187

hence probability =187/500=0.374

N(T)= 500 N(A)= 194 N(B)= 224 N(C)= 201 N(AnB)= 104 N(BnC)= 61 N(AnC)= 82 N(AUB)= 314 N(BUC)= 364 N(AUC)= 313 N(AnBnC) = 33

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