Conditional+Probability+with+diagrams


 * Conditional Probability**


 * Unit goal:** Students __#|apply__ their earlier experience with two-way tables to build formal understanding of conditional probability and connect two-way tables, Venn diagrams and tree diagrams and interpret.

S.CP. 3 Understand the conditional probability of A given B as P(A and B)/P(B).
 * Content Standards **

S.CP.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to… approximate conditional probabilities.

S.CP.5 Recognize and explain the concepts of conditional probability…in everyday language and everyday situations.

The goal of this task is for students to connect two-way tables with Venn diagrams and begin to develop an understanding of conditional probability.
 * Task 1-Develop Understanding “Skittles or Snickers?”**

Launch Explore Discuss
 * Hand out a slip of __#|paper__ to each student.
 * Have them write their gender on the paper along with which of the following treats they prefer: Snickers or Skittles. Make sure their votes are anonymous and private.
 * Collect the data and tally.
 * Put students into groups and hand out part 1 of Skittles or Snickers.
 * Students work together to answer questions and __#|fill out__ the two-way table.
 * Select students to share their __#|work__with the class in an order that will help build the following concepts.
 * How __#|to fill out__ the joint frequencies and how to find the marginal frequencies in the table
 * Notation of P(boy), P(snickers), P(snickers and boy), P(snickers|boy)
 * The importance of language and the difference between “and,” and “given.”
 * The process used to find the different probabilities.

Launch Explore Discuss The goal of this task is to connect Venn diagrams, Two-way tables, and Tree diagrams while reviewing conditional probability and the general addition rule.
 * Hand out part 2 of Skittles or Snickers.
 * Students work together to fill out Venn diagram and answer questions.
 * How they determined categories for the Venn diagram
 * How to calculate the numbers for the diagram
 * How they found the probabilities from the Venn diagram as opposed to the two-way table. Make other connections between the Venn diagram and the two-way table.
 * Task 2-Solidify “Mathis Cool High School”**

Launch Explore Discuss
 * Hand out Part 1 of Mathis Cool High School
 * Students work in groups to create a two-way table from the Venn diagram and answer the questions
 * Find the percent of students in neither
 * Correct rows and columns in the two-way table
 * Methods of calculating probabilities

Launch Explore Discuss
 * Hand out Part 2 of Mathis Cool High School
 * Students work in groups to create a tree diagram with the probabilities and to answer the final question
 * In finding the second branch of the tree diagram, make sure the probabilities are conditional.
 * To find P(Student Council and Math Club) you have to multiply across the braches of the tree diagram;
 * Perhaps that you have to discuss the need to subtract the intersection that was counted twice in the general addition rule.
 * Point out information in each diagram that is helpful in calculating the probability and make other connections between the three diagrams.


 * Task 3-Practice “Representing Data”**

The goal of this task is to deepen understanding and connections discussed in this unit and help the students __#|start__ with a story problem and move to using the techniques of displaying data to help them calculate probabilities.

Launch Explore Discuss:
 * Hand out task in three parts. You may choose to have a short discussion between each part or wait until all three are completed.
 * Students work together to deepen their understanding and make connections between the three types of displaying data and finding conditional probabilities
 * Select students to share their work. Part 3 will have different methods of solving.