# Probability Topics

## Two Basic Rules of Probability

In calculating probability, there are two rules to consider when you are determining if two events are independent or dependent and if they are mutually exclusive or not.

### The Multiplication Rule

If A and B are two events defined on a sample space, then P(A AND B) = P(B)P(A|B).
This equation can be rewritten as P(A AND B) = P(B)P(A|B), the multiplication rule.
If A and B are independent, then P(A|B) = P(A). In this special case, P(A AND B) = P(A|B)P(B) becomes P(A AND B) = P(A)P(B).
A bag contains four green marbles, three red marbles, and two yellow marbles. Mark draws two marbles from the bag without replacement. The probability that he draws a yellow marble and then a green marble is
Notice that 
 
  . After the yellow marble is drawn, there are four green marbles in the bag and eight marbles in all.

### The Addition Rule

If A and B are defined on a sample space, then P(A OR B) = P(A) + P(B) − P(A AND B).
Draw one card from a standard deck of playing cards. Let H = the card is a heart, and let J = the card is a jack. These events are not mutually exclusive because a card can be both a heart and a jack.
If A and B are mutually exclusive, then P(A AND B) = 0. Then P(A OR B) = P(A) + P(B) − P(A AND B) becomes P(A OR B) = P(A) + P(B).
Draw one card from a standard deck of playing cards. Let H = the card is a heart and S = the card is a spade. These events are mutually exclusive because a card cannot be a heart and a spade at the same time. The probability that the card is a heart or a spade is

### References

Baseball Almanac. (2013). Retrieved from www.baseball-almanac.com
DiCamillo, Mark, and Field, M. The file poll. Field Research Corporation. Retrieved from http://www.field.com/fieldpollonline/subscribers/Rls2443.pdf
Field Research Corporation. (n.d.). Retrieved from www.field.com/fieldpollonline
Forum Research. (n.d.). Mayors approval down. Retrieved from http://www.forumresearch.com/forms/News Archives/News Releases/74209_TO_Issues_-_Mayoral_Approval_%28Forum_Research%29%2820130320%29.pdf
Rider, D. (2011, Sept. 14). Ford support plummeting, poll suggests. The Star. Retrieved from http://www.thestar.com/news/gta/2011/09/14/ford_support_plummeting_poll_suggests.html
Shin, H. B., and Kominski, R. A. (2010 April). Language use in the United States: 2007 (American Community Survey Reports, ACS-12). Washington, DC: United States Census Bureau. Retrieved from http://www.census.gov/hhes/socdemo/language/data/acs/ACS-12.pdf
The Roper Center for Public Opinion Research. (n.d.). Archives. Retrieved from http://www.ropercenter.uconn.edu/
The Wall Street Journal. (n.d.). Retrieved from https://www.wsj.com/
U.S. Census Bureau. (n.d.). Retrieved from https://www.census.gov/
Wikipedia. (n.d.). Roulette. Retrieved from http://en.wikipedia.org/wiki/Roulette

### Chapter Review

The multiplication rule and the addition rule are used for computing the probability of A and B, as well as the probability of A or B for two given events A, B defined on the sample space. In sampling with replacement, each member of a population is replaced after it is picked, so that member has the possibility of being chosen more than once, and the events are considered to be independent. In sampling without replacement, each member of a population may be chosen only once, and the events are considered to be not independent. The events A and B are mutually exclusive events when they do not have any outcomes in common.

### Formula Review

The multiplication rule—P(A AND B) = P(A|B)P(B)
The addition rule—P(A OR B) = P(A) + P(B) − P(A AND B)
Use the following information to answer the next 10 exercises. Forty-eight percent of all voters of a certain state prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Among Latino registered voters in this state, 55 percent prefer life in prison without parole over the death penalty for a person convicted of first-degree murder. Of all citizens in this state, 37.6 percent are Latino.
In this problem, let

Suppose that one citizen is randomly selected.

### Homework

.  A local restaurant sells pork chops and chicken breasts.  The given values below are the weights (in ounces) of pork chops and chicken breasts listed on the menu.  Your server will randomly select one piece of meat (pork chop or chicken breast) that you will be served.