CK-12 Probability and Statistics - Advanced

3.4. Conditional Probability http://www.ck12.org

Lesson Summary

1. IfAandBare two events, then the probability of the eventAto occur, given that eventBoccurs is called a
   conditional probability. We denote it by the symbolP(A|B),which reads "the probability ofAgivenB."


2. Conditional probability can be found with the equationP(A|B) =P(PA(∩BB)).

Review Questions

1. IfP(A) = 0. 3 ,P(B) = 0. 7 ,andP(A∩B) = 0. 15 ,FindP(A|B)andP(B|A).


2. Two fair coins are tossed. i. List the possible outcomes in the sample space. ii. Two events are defined as
   follows:

A:{At least one head appears}

B:{Only one head appears}

FindP(A),P(B),P(A∩B),P(A|B),andP(B|A)

3. A box of six marbles contains two white, two red, and two blue. Two marbles are randomly selected without
   replacement and their colors are recorded. i. List the possible outcomes in the sample space. ii. Let the
   following events be defined:

A:{Both marbles have the same color}

B:{Both marbles are red}

C:{At least one marble is red or white}

FindP(B|A),P(B|A′),P(B|C),P(A|C),andP(C|A′)

Review Answers

1. 
   
   
   
   0. 21 , 0. 5
   
   
   
   


2. 3/ 4 , 1 / 2 , 1 / 2 , 1 , 2 / 3


3. 1/ 3 , 0 , 1 / 14 , 1 / 7 , 1