# Probability Topics

## Contingency Tables

A two-way table provides a way of portraying data that can facilitate calculating probabilities. When used to calculate probabilities, a two-way table is often called a contingency table. The table helps in determining conditional probabilities quite easily. The table displays sample values in relation to two different variables that may be dependent or contingent on one another. We used two-way tables in Chapters 1 and 2 to calculate marginal and conditional distributions. These tables organize data in a way that supports the calculation of relative frequency and, therefore, experimental (empirical) probability. Later on, we will use contingency tables again, but in another manner.

### References

American Red Cross. (2013). Blood Types. Retrieved from http://www.redcrossblood.org/learn-about-blood/bloodtypes
Centers for Disease Control and Prevention/National Center for Health Statistics, United States Department of Health and Human Services. (n.d.). Retrieved from https://www.cdc.gov/nchs/
Haiman, C. A., et al. (2006, Jan. 26). Ethnic and racial differences in the smoking-related risk of lung cancer. The New England Journal of Medicine. Retrieved from http://www.nejm.org/doi/full/10.1056/NEJMoa033250
Samuels, T. M. (2013). Strange facts about RH negative blood. eHow Health. Retrieved from http://www.ehow.com/facts_5552003_strange-rh-negative-blood.html
The Disaster Center Crime Pages. (n.d.). United States: Uniform crime report  state statistics from 19602011. Retrieved from http://www.disastercenter.com/crime/
United Blood Services. (2011). Human blood types. Retrieved from http://www.unitedbloodservices.org/learnMore.aspx
United States Senate. (n.d.). Retrieved from www.senate.gov

### Chapter Review

There are several tools you can use to help organize and sort data when calculating probabilities. Contingency tables, also known as two-way tables, help display data and are particularly useful when calculating probabilites that have multiple dependent variables.

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Use the following information to answer the next four exercises.  shows a random sample of musicians and how they learned to play their instruments.

### Bringing It Together

Use the following information to answer the next seven exercises. An article in the , reported about a study of people who use a product in California and Hawaii. In one part of the report, the self-reported ethnicity and using the product levels per day were given. Of the people using the product at most 10 times a day, there were 9,886 African Americans, 2,745 Native Hawaiians, 12,831 Latinos, 8,378 Japanese Americans, and 7,650 whites. Of the people using the product 11 to 20 times per day, there were 6,514 African Americans, 3,062 Native Hawaiians, 4,932 Latinos, 10,680 Japanese Americans, and 9,877 whites. Of the people using the product 21 to 30 times per day, there were 1,671 African Americans, 1,419 Native Hawaiians, 1,406 Latinos, 4,715 Japanese Americans, and 6,062 Whites. Of the people using the product at least 31 times per day, there were 759 African Americans, 788 Native Hawaiians, 800 Latinos, 2,305 Japanese Americans, and 3,970 whites.

### Homework

Use the information in the  The table shows the political party affiliation of each of 67 members of the U.S. Senate in June 2012, and when they would next be up for reelection.



Use the following information to answer the next two exercises. The table of data obtained from  shows hit information for four well-known baseball players. Suppose that one hit from the table is randomly selected.