CCSS.Math.Content.HSS-CP.A.2
The standard
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.
Common Core State Standards for Mathematics
What this standard means
Students need to decide whether two events are independent by comparing two values: the probability that both happen, and the product of their separate probabilities. They should read probabilities from tables, lists, or descriptions, then check whether P(A and B) = P(A) × P(B).
Mastery looks like using the rule correctly and explaining the result in context, not just saying “yes” or “no.” Students often mix up “and” with “or,” assume events are independent because they seem unrelated, or forget to use the total group when finding each probability.
Ways to teach it
- Give students a two-way table of survey results and have them calculate P(A), P(B), and P(A and B) with calculators or fraction strips.
- Ask students to write: How can two events seem connected but still fail the independence test?
- Use an exit ticket with one small two-way table and ask students to decide if two listed events are independent.
- Compare drawing a card and rolling a die with choosing a student’s grade level and club membership from your school data.
Plan a lesson for CCSS.Math.Content.HSS-CP.A.2
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Related standards
- CCSS.Math.Content.HSS-CP.A
Understand independence and conditional probability and use them to interpret data
- CCSS.Math.Content.HSS-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 gi...
- CCSS.Math.Content.HSS-CP.B.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.
- CCSS.Math.Content.HSS-CP.A.5
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.