CCSS.Math.Content.HSS-CP.A.5
The standard
Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
Common Core State Standards for Mathematics
What this standard means
Students need to tell the difference between “the chance of A given B” and “the chance of B given A.” They should use plain language, tables, and percentages to explain how knowing one fact can change the chance of another. They also need to decide when two events seem independent, meaning one event does not change the chance of the other.
Mastery looks like reading a two-way table and making a clear comparison without flipping the condition. Students often get stuck by treating both directions as the same, ignoring the base group, or using raw counts when percentages are needed.
Ways to teach it
- Give pairs a two-way table from colored counters in bags, then have them calculate and compare two conditional probabilities.
- Ask students to explain whether “likes soccer given they play an instrument” means the same as “plays an instrument given they like soccer.”
- Use an exit ticket with one two-way table and ask for two conditional probability statements plus one independence claim.
- Have students analyze a school survey table about homework, activities, and sleep, then identify which relationships seem dependent or independent.
Plan a lesson for CCSS.Math.Content.HSS-CP.A.5
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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.9
(+) Use permutations and combinations to compute probabilities of compound events and solve problems.
- CCSS.Math.Content.HSS-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 characte...