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= E4: Interpret and compute conditional probabilities =

=**What you should know:**=

**Conditional Probability:** is the probability of an event occurring when you know another event occurs.

 * Equation: P(A)=P(A|B) The probability event A occurs given that event B occurs**.

In Conditional Probability you look at different situations that have display certain conditions.

Example: The preference of a snack at a sports game
= = =**Things to think about:**=
 * || **Ice Cream** || **Pretzels** || **Total** ||
 * =Soccer= || =45= || =87= || =132= ||
 * =Football= || =65= || =36= || =101= ||
 * =Total= || =110= || =123= || =233= ||

Suppose you pick someone at random from the total number of people who attend these sports games, and find the following probabilities.
1.) P(prefers ice cream) Answer: P=110/233 //is the answer because you are looking for the probability that someone likes ice cream, look at the ice cream total and then you would put that number over however many people total.//

2.) P(prefers Football) //Answer: P=101/233 is the answer because you are just looking for the probability that someone just likes football, then you take that number (101) and you would put that over the total number of people in general//

3.( P(prefers ice cream | likes football) Answer: P= 65/101 is the answer because you are just focusing on the column dealing with ice cream, then you would look at the section that deals with ice cream and deals with football. which is 65 then you take that number and put it over the total number of people.

=**A term that you may need to know..**=

Ex. Are the events someone who likes ice cream but prefers soccer are mutually exclusive? Answer: Yes, they are mutually exclusive because you can like ice cream and prefer soccer. They do not run in to each other you can have both.
 * Mutually Exclusive:** Is when two events cannot happen at the same time (Ex. Monday //and// Friday)

= Problems that you might run into.. =


 * Some common mistakes that occur when you are dealing with conditional probability are:**
 * **The definition of "Mutually Exclusive"**
 * **Reading the table the right way according to the question (rows and columns)**


 * Say you get a problem like this:** P(prefers ice cream | likes football) you would only focus on the row dealing with football, and the "given prefers ice cream" would amount to be 65/101 because you have ice cream and football, then you would take the total number in the football row and put it under the 65 for the fraction.
 * || **Ice Cream** || **Pretzels** || **Total** ||
 * = Soccer = || = 45 = || = 87 = || = 132 = ||
 * = Football = || = 65 = || = 36 = || = 101 = ||
 * = Total = || = 110 = || = 123 = || = 233 = ||


 * Or you get a problem like this:** P(prefers ice cream) you would only use the column that has to do with ice cream, and you would take the total of the ice cream column and put it over the over all total 110/233


 * || **Ice Cream** || **Pretzels** || **Total** ||
 * = Soccer = || = 45 = || = 87 = || = 132 = ||
 * = Football = || = 65 = || = 36 = || = 101 = ||
 * = Total = || = 110 = || = 123 = || = 233 = ||

=***For more information you can visit [|this] website, it goes more in depth about conditional probability shows different forms of conditional probability like equations.**=