Students formalize their understanding of compound probability, develop an understanding of conditional probability, and understand and calculate permutations and combinations.
In Unit 8, Probability, students extend their understanding of probability from seventh grade to a more formal approach to probability by applying formulas and definitions.
Students begin the unit using visual representations of lists, tree diagrams, and Venn diagrams to find the probability of events that intersect or represent the union or complement of outcomes. Students also formalize their understanding of compound probability. Then, students develop a conceptual and procedural understanding of conditional probability and how this can be used to determine whether variables are independent. In application, students use this knowledge to solve a set of applications on medical testing. Finally, as an optional part of the unit (covering plus (+) Common Core State Standards), students understand and calculate permutations and combinations. The students develop an understanding that whether order matters or not can affect the sample space of the total combinations or the number of chosen items within a set of items.
In Algebra 2, students will continue their study of probability by studying statistical inference and making decisions using probability.
This assessment accompanies Unit 8 and should be given on the suggested assessment day or after completing the unit.
?
Internalization of Standards via the Unit Assessment
Internalization of Trajectory of Unit
?
?
sample space | $$P$$ (desired outcome) |
complement | tree diagram |
with replacement | without replacement |
mutually exclusive (disjoint) | addition rule |
multiplication rule | equally likely (fair) |
compound probability | venn diagram |
conditional probability | dependent event |
independent event | relative frequency |
two-way table | medical testing |
false positive/false negative | true positive/true negative |
permutation | combination |
fundamental counting principle |
?
7.SP.C.8
S.CP.A.1
Describe the sample space of an experiment or situation. Use probability notation to identify the “and,” “or,” and complement outcomes from a given sample space.
7.SP.C.7
S.CP.A.2
S.CP.A.4
S.CP.B.6
S.CP.B.7
Determine the probability of events with replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
7.SP.C.7
S.CP.A.2
S.CP.B.6
S.CP.B.7
S.CP.B.8
Determine the probability of events without replacement using tree diagrams, addition rules for mutually exclusive events, and multiplication rules for compound events.
S.CP.A.1
S.CP.A.2
S.CP.B.7
Determine the probability of events that are not mutually exclusive to formalize the addition rule.
S.CP.A.3
Describe conditional probability and develop the rule $$P(B|A)=\frac{P(A \space \mathrm{and} \space B)}{P(A)}$$.
S.CP.A.2
S.CP.A.3
S.CP.A.5
Determine whether events are independent.
S.ID.B.5
S.CP.A.4
S.CP.A.5
Calculate and analyze relative frequencies in two-way tables to make statements about the data and determine independence.
S.CP.A.3
S.CP.A.4
S.CP.A.5
Make decisions about medical testing based on conditional probabilities.
S.CP.B.9
Describe and apply the counting principle and permutations to contextual and non-contextual situations.
S.CP.B.9
Describe and apply the counting principle and combinations to contextual and non-contextual situations.
Key: Major Cluster Supporting Cluster Additional Cluster
?
?
?