Tree Diagrams If you toss a fair coin twice, what’s the probability you get two heads?
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Transcript of Tree Diagrams If you toss a fair coin twice, what’s the probability you get two heads?
WarmUp
Homework Questions
5.3 ContinuedTree Diagrams
If you toss a fair coin twice, what’s the probability you get two heads?
What is a tree diagram?
Handedness
Female Male
Left 3 1
Right 18 6
Example Suppose we select two students at random.
◦ Draw a tree diagram that shows the sample space for this chance process.
◦ Find the probability that both students are left handed.
The Pew Internet and American Life Project finds that 93% of teenagers (ages 12 to 17) use the internet, and that 55% of online teens have posted a profile on a social networking site.
What percent of teens are online and have posted a profile? Explain.
Example
About 27% of adult Internet users are 18 to 29 years old, another 45% are 30 to 49 years old, and the remaining 28% are 50 and over. The Pew Internet and American Life Project finds that 70% of Internet users aged 18-29 have visited a video-sharing site, along with 51% of those aged 30-49 and 26% of those 50 and over. Do most internet users visit YouTube and similar sites?
State: What percent of all adult Internet users visit video-sharing sites?
Plan: restate…
Who Visits YouTube?
Tree Diagram
What if I asked what percent of adult internet users who visit video-sharing sites are aged 18-29?
Working backwards…
To test for HIV, clinics use “rapid tests” that give a result while the client waits. The tradeoff for fast results is that rapid tests are less accurate. Applied to people who have no HIV antibodies, one rapid test has probability about 0.004 of producing a false positive. If a clinic tests 200 people who are free of HIV antibodies, what is the chance that at least one false positive will occur?
Finding the probability of “at least one”
Over 10,000 athletes competed in the Olympic games in Beijing. A committee administered more than 5000 drug tests to athletes. Suppose 2% of athletes had actually taken (banned) drugs. Suppose that the testing procedure used had a false positive rate of 1% and a false negative rate of 0.5%. What’s the probability that an athlete who tests positive actually took drugs?
Athletes and Drug Testing
Section 5.3 homework: Pg. 329 (63, 65, 67-78, 81, 83-88, 94-96, 99-103)
Homework
