AP Statistics Section 6.3C More Conditional Probability

Example: Assume that 1.3% of AHS students smoke on a daily basis. A breath test is designed to determine if someone has smoked in the last week. Assume the test will come back positive 96% of the time if someone has smoked in the last week but will also come back positive 7% of the time if someone has not smoked in the last week (a false positive). Find the probability that a randomly selected student at AHS has smoked in the last week if the test comes back positive? We will use a tree diagram to organize our thinking.

Assume that 1.3% of AHS students smoke on a daily basis. A breath test is designed to determine if someone has smoked in the last week. Assume the test will come back positive 96% of the time if someone has smoked in the last week but will also come back positive 7% of the time if someone has not smoked in the last week (a false positive). Find the probability that a randomly selected student at AHS has smoked in the last week if the test comes back positive? We will use a tree diagram to organize our thinking.

Example: Online chat rooms are dominated by the young. Teens are the biggest users. If we look only at adult internet users (aged 18 and older), 47% of the 18 to 29 age group chat, as do 21% of those aged 30 to 49 and just 7% of those 50 and over. To learn what percent of all adult internet users participate in chat rooms, we also need the age breakdown of users: 29% of adult users are aged 18 to 29, 47% are aged 30 to 49 and 24% are 50 and over. We will use a tree diagram to organize our thinking.

Are the events “18-29 year old internet user” and “adult chat room user” independent”?