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. positive .96 .013 AHS Students .987 smoke negative .04 .07 positive don' t smoke .93 negative 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. .96 .013 AHS Students .987 smoke .04 .07 positive .01248 negative .00052 positive .06909 negative .91791 don' t smoke .93 P( smoked / positve) smoked positive .01248 . 01248 . 06909 positive .153 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. Chat .47 No .53 18 29 .29 .1537 Chat .21 .0987 No .79 .3713 30 49 .47 over 50 .24 .1363 Chat .07 No .93 .0168 .2232 Are the events “18-29 year old internet user” and “adult chat room user” independent”? P(18 29 chat ) .1363 P(18 29 / chat ) .5413 .2518 P(chat ) P(18 29) .29 P(18 29) P(18 29 / chat ) .29 .5413 NO