Unit 8a: Probability & Statistics (Compound Events & Expected Values) |
Probabilistic Reasoning (PR) G.PR.10: Solve problems involving the probability of compound events to make informed decisions; interpret expected value and measures of variability to analyze probability distributions. |
STANDARD & Expectations | LT & SC Lesson Activities & Resources |
G.PR.10.1 Describe categories of events as subsets of a sample space using unions, intersections, or complements of other events. Apply the Addition Rule conceptually, P(A or B) = P(A) + P(B) -P(A and B), and interpret the answers in context. | LT:
SC: I can communicate informed decisions by applying the Addition Rule to a problem involving the probability of compound events. I can use Venn Diagrams and two-way tables to help visualize events. I can use two-way tables to reveal the sample space. I can use Venn Diagrams to show intersections of two or more events.
LA&R: |
G.PR.10.2 Apply and interpret the general Multiplication Rule conceptually to independent events of a sample space, P(A and B) = [P(A)]x[P(B|A)] = [P(B)]x[P(A|B)] using contingency tables or tree diagrams. | LT:
SC: I can relate the conditional probability back to the conceptual interpretation of probability studied in previous courses. I understand the Multiplication Rule conceptually with limited emphasis on the manipulation of the equation. I can use a tree diagram to help me visualize events and probabilities of those events.
LA&R: |
G.PR.10.3 Use conditional probability to interpret risk in terms of decision-making and investigate questions such as those involving false positives or false negatives from screening tests. | LT: I am learning to use conditional probability to interpret risk in terms of decision-making. I am learning to investigate questions such as those involving false positives or false negatives from screening tests.
SC: I can answer relevant questions based on the appropriate risk measures. I can explain how studies and/or models are used to determine risk measures. I can recognize the chances of a false positive or a false negative is not the same as the chances of having the condition or not having the condition given the test result. I can interpret and communicate the consequences of making the false positive or false negative errors. I can interpret the notation for conditional probability in context.
LA&R: |
G.PR.10.4 Define permutations and combinations and apply this understanding to compute probabilities of compound events and solve meaningful problems. | LT: I am learning to define permutations and combinations. I am learning to compute probabilities of compound events using permutations and combinations. I am learning to solve meaningful problems.
SC: I understand the terms permutation and combination. I can solve simple problems involving selection and arrangement of objects in a line, including those involving repetition and restriction. I understand and can apply permutations and combinations. I can interpret formal notation to communicate about combinations and permutations
LA&R: |
G.PR.10.5 Interpret the probability distribution for a given random variable and interpret the expected value. | LT:
SC: I understand that the probabilities in a distribution are between 0 and 1, and that they should sum to 1. I can define a random variable and understand that the sample space consists of all the values the random variable can take. I can explore and develop an understanding that the expected value is the mean of the probability distribution. I can solve real-life problems given the expected value and interpret its meaning within context.
LA&R: |
G.PR.10.6 Develop a probability distribution for variables of interest using theoretical and empirical (observed) probabilities and calculate and interpret the expected value. | LT:
SC: I can calculate the probability of all possible outcomes of a given event and display the probability of each graphically. I understand the sum of all probabilities within one distribution will be 1 (100%). I can find the probability of a certain quantity. I can find the probability of a range of quantities.
LA&R: |
G.PR.10.7 Calculate the expected value of a random variable and interpret it as the mean of a given probability distribution. | LT:
SC: I can use the expected value of a random variable to make informed decisions. I can calculate the expected value of a random variable as the sum of each Xn*PXn. I understand the sum is a weighted average of the outcomes (weighted by the probability).
LA&R: |
G.PR.10.8 Compare the payoff values associated with the probability distribution for a random variable and make informed decisions based on expected value and measures of variability. | LT: I am learning to compare the payoff values associated with the probability distribution for a random variable. I am learning to make informed decisions based on expected value and measures of variability.
SC: I can make decisions about real-life problems considering net value or payoff. I can understand that two probability distributions can have the same expected value, but one may vary more than the other, and this should be considered in decision-making. I can compute and interpret expected values for games of chance, insurance policies, and other real-life situations.
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Unit 8b: Categorical Data in two-way frequency tables; conditional probability |
Data & Statistical Reasoning (DSR); Probabilistic Reasoning (PR) G.DSR.11: Examine real-life situations presented in two-way frequency tables to calculate probabilities, to model categorical data, and to explain real-life phenomena. |
STANDARD & Expectations | LT & SC Lesson Activities & Resources |
G.DSR.11.1 Construct and summarize categorical data for two categories in two-way frequency tables. | LT:
SC: I can identify, calculate, and interpret joint, marginal, and conditional relative frequencies in context of the data. I can analyze meaningful, real-life data and recognize possible associations and trends in the data. I can understand and apply concepts of sample space to describe categorical data.
LA&R: |
G.DSR.11.2 Use categorical data in two-way frequency tables to calculate and interpret probabilities based on the investigation. | LT:
SC:
LA&R: |
