Question

In a recent study on teenage drug and alcohol use, researchers found that one in ten teenagers admitted to using marijuana al least once a month, one in five admitted to drinking alcohol at least once a week, and one in four admitted to smoking cigarettes on a daily basis. The researchers also found that 10% of respondents admitted to both smoking cigarettes daily and drinking alcohol at least once a week; 5% of respondents admitted to both smoking cigarettes daily and using marijuana at least once a month; 3% of respondents admitted to both drinking alcohol at least once a week and using marijuana at least once a month; and 1% of respondents admitted to doing all three. A rapidly graying middle-aged parent reading these statistics becomes very concerned that his teenager, who took part in the study and whom he considers to be as likely as any of the others to engage in such behaviors, may be at serious risk. With the aid of a Venn diagram find the probability that the teenager

a. does not engage in any of these behaviors?

b. engages in exactly one of these three behaviors?

Answer 1