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COMMON CORE OBJECTIVES S.CP.A.1 TO S.CP.A.3

S.CP.A.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.A.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.A.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.

COMMON CORE OBJECTIVES S.CP.A.4 TO S.CP.A.6

S.CP.A.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.A.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.A.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.

COMMON CORE OBJECTIVES S.CP.B.7 TO S.CP.B.9

S.CP.B.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.B.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.B.9 Use permutations and combinations to compute probabilities of compound events and solve problems.

 (1) This first week is all about setting the stage for the following weeks of probability.  We will investigate sample spaces, uniform probability, and the fundamental counting principle. (2) This week will be about putting a picture to probability using Venn Diagrams.  Venn diagrams provide a great support to students to see and understand intersections, unions and probability. (3) The basics lead us into probably the most important concept of the unit – independence.  We look the basic independence rule for multiplication and then look at independence of in conditional statements. (4) Two way frequency tables form a nice way to consolidate all of the things learned so far.  In two way tables we will determine basic probabilities, conditional probabilities and independence.  HSS.CP.A.5 has the student explore the world around them. (5) HONORS ONLY – Finally, we look into permutation and combinations to calculate more complex sample spaces.  (*S.CP.B.9 is an honors objective) We then use permutations and combinations to help us determine probabilities.