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
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students explain how knowing one event happened can change the chance of another event. They decide whether two events are independent and distinguish “A given B” from “B given A.”
What Mastery Looks Like
- Given a table or everyday scenario, a student identifies the relevant subgroup and compares conditional rates. The student explains independence by stating whether one event changes the probability of the other.
Common Misconceptions
- Students often reverse P(A given B) and P(B given A). They may treat any two events that can occur together as independent. They also compare raw counts instead of rates when groups differ in size.
How to Assess It
- Exit ticket: In a school, 30 of 50 bus riders and 20 of 50 non-bus riders arrive before 8:00. Does riding the bus appear independent of arriving early? Explain using the two rates.
Lesson moves
Ways to Teach It
Give groups two bags of colored tiles, have them draw with stated conditions, and compare how the condition changes the sample space.
Ask students to write: Is the chance of rain given clouds the same as the chance of clouds given rain? Defend your answer.
Run a card sort matching everyday scenarios to “independent,” “dependent,” or “reversed condition,” then have partners justify each match.
Give students a fictional sports roster and grade-level table to compare team membership given grade with grade given team membership.
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Printable HSS-CP.A.5 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.HSS-CP.A.5, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetLearning progression
Where This Standard Sits
Before This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.HSS-CP.A.1
Conditional probability and independence rely on identifying events and their overlap, but can be introduced informally through everyday situations.
- CCSS.Math.Content.HSS-CP.A.3
Formal conditional probability and independence give students the meanings they must translate into everyday situations and explanations.
- CCSS.Math.Content.HSS-CP.A.2
The product rule gives a precise test for independence that students can translate into everyday explanations of related events.
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