# Probability Topics

## Tree and Venn Diagrams

Sometimes, when the probability problems are complex, it can be helpful to graph the situation. Tree diagrams and Venn diagrams are two tools that can be used to visualize and solve conditional probabilities.

### Tree Diagrams

A tree diagram is a special type of graph used to determine the outcomes of an experiment. It consists of branches that are labeled with either frequencies or probabilities. Tree diagrams can make some probability problems easier to visualize and solve. The following example illustrates how to use a tree diagram:

### Venn Diagram

A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events.

### References

American Cancer Society. (n.d.). Retrieved from https://www.cancer.org/
Clara County Public Health Department. (n.d.). Retrieved from https://www.sccgov.org/sites/sccphd/en-us/pages/phd.aspx
Federal Highway Administration, U.S. Department of Transportation. (n.d.). Retrieved from https://www.fhwa.dot.gov/
The Data and Story Library. (1996). Retrieved from http://lib.stat.cmu.edu/DASL/
The Roper Center for Public Opinion Research. (2013). Search for datasets. Retrieved from http://www.ropercenter.uconn.edu/data_access/data/search_for_datasets.html
USA Today. (n.d.). Retrieved from https://www.usatoday.com/
U.S. Census Bureau. (n.d.). Retrieved from https://www.census.gov/
World Bank Group. (2013). Environment. Available online at http://data.worldbank.org/topic/environment

### Chapter Review

A tree diagram uses branches to show the different outcomes of experiments and makes complex probability questions easy to visualize.
A Venn diagram is a picture that represents the outcomes of an experiment. It generally consists of a box that represents the sample space S together with circles or ovals. The circles or ovals represent events. A Venn diagram is especially helpful for visualizing the OR event, the AND event, and the complement of an event and for understanding conditional probabilities.

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### Homework

Use the following information to answer the next two exercises. This tree diagram shows the tossing of an unfair coin followed by drawing one bead from a cup containing three red (R), four yellow (Y), and five blue (B) beads. For the coin, P(H) = 
  and P(T) = 
  where H is heads and T is tails.

### Bringing It Together

Use the following information to answer the next two exercises. Suppose that you have eight cards. Five are green and three are yellow. The cards are well shuffled.
Use the following information to answer the next two exercises. The percent of licensed U.S. drivers (from a recent year) who are female is 48.60. Of the females, 5.03 percent are age 19 and under; 81.36 percent are age 20–64; 13.61 percent are age 65 or over. Of the licensed U.S. male drivers, 5.04 percent are age 19 and under; 81.43 percent are age 20–64; 13.53 percent are age 65 or over.