Suppose that in a senior college class of 500500 ​students, it is found that 179179 ​smoke, 228228 drink alcoholic​ beverages, 191191 eat between​ meals, 9999 smoke and drink alcoholic​ beverages, 5959 eat between meals and drink alcoholic​ beverages, 7272 smoke and eat between​ meals, and 3030 engage in all three of these bad health practices. If a member of this senior class is selected at​ random, find the probability that the student​ (a) smokes but does not drink alcoholic​ beverages; (b) eats between meals and drinks alcoholic beverages but does not​ smoke; (c) neither smokes nor eats between meals.

Answer: a) 0.16, b) 0.058, and c) 0.856.Step-by-step explanation:Since we have given that Number of students = 500Number of students smoke = 179Number of students drink alcohol = 228Number of students eat between meals = 119Number of students eat between meals and drink alcohol = 59Number of students eat between meals and smoke = 72Number of students engage in all three = 30 a) Probability that the student smokes but does not drink alcohol is given by[tex]P(S-A)=P(S)-P(S\cap A)\\\\P(S-A)=\dfrac{179}{500}-\dfrac{99}{500}\\\\P(S-A)=\dfrac{179-99}{500}\\\\P(S-A)=\dfrac{80}{500}\\\\P(S-A)=0.16[/tex]b) eats between meals and drink alcohol but does not smoke.[tex]P((M\cap A)-S)=P(M\cap A)-P(M\cap S\cap A)\\\\P((M\cap A)-S)=\dfrac{59}{500}-\dfrac{30}{500}\\\\P((M\cap A)-S)=\dfrac{59-30}{500}\\\\P((M\cap A)-S)=\dfrac{29}{500}\\\\P((M\cap A)-S)=0.058[/tex]c) neither smokes nor eats between meals.[tex]P(S'\cap M')=1-P(S\cup M)\\\\P(S'\cap M')=1-\dfrac{72}{500}\\\\P(S'\cap M')=\dfrac{500-72}{500}\\\\P(S'\cap M')=\dfrac{428}{500}=0.856[/tex]Hence, a) 0.16, b) 0.058, and c) 0.856.