4.+Applications+of+Probability

Standards
S.CP.1. Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events (“or,” “and,” “not”). ⋆ S.CP. 2. Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent. ⋆ S.CP.3. Understand the conditional probability of A given B as P(A and B)/P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B. ⋆ 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 decide if events are independent and to approximate conditional probabilities. For example, collect data from a random sample of students in your school on their favorite subject among math, science, and English. Estimate the probability that a randomly selected student from your school will favor science given that the student is in tenth grade. Do the same for other subjects and compare the results. ⋆ S.CP.5. Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations. For example, compare the chance of having lung cancer if you are a smoker with the chance of being a smoker if you have lung cancer. ⋆ S.CP.6. Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model. ⋆ S.CP.7. Apply the Addition Rule, P(A or B)=P(A)+P(B)−P(A and B), and interpret the answer in terms of the model. ⋆ S.CP.8. (+) Apply the general Multiplication Rule in a uniform probability model, P(A and B)=P(A)P(B|A)=P(B)P(A|B), and interpret the answer in terms of the model. ⋆ S.CP.9. (+) Use permutations and combinations to compute probabilities of compound events and solve problems. ⋆

S.MD.6. (+) Use probabilities to make fair decisions (e.g., drawing by lots, using a random number generator). ⋆ S.MD.7.(+) Analyze decisions and strategies using probability concepts (e.g., product testing, medical testing, pulling a hockey goalie at the end of a game). ⋆

Examples of Learning Cycles and Tasks
Applications of Probability Learning Cycle -- learning cycle from Core Academy

Probability Goals (No.Davis CA, refers to II.4.S.CP-1,2,3,4,5,6,7)

Probability Rules and Independence (No. Davis CA, refers to ?)

Conditional Probability - http://probabilityunit.wikispaces.com/ (? CA, refers to ?)

Conditional Probability (Orem, Jenn, Jeremy, Allison, Megan, Larry)

Independant/Conditional Probability, (Snow Canyon CA, refers to ?)

Using Venn Diagrams for Disjointed and Joined Conditions (JIm, Bill, Becky, Ramona)

Conditional and Independent Events (Wasatch CA, refers to C.SP.5)

Independent vs. Dependent (Wasatch CA, refers to S.CP.3

Conditional Probability with diagrams ( Salem Hills CA)

Conditional Probability (Copper Hills High School CA)

Conditional Probability and Testing (West High CA, refers to C.SP.3,5,6)

Sample Spaces and Subsets (Cache County, UT refers to S.CP.1)

Independent and Dependent Events (West High CA, refers to S.CP.2)

Determining Independence and Dependence ( Cache County, UT refers to S.CP.2)