CCSS.Math.Content.HSS-CP.B.6
The standard
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.
Common Core State Standards for Mathematics
What this standard means
Students need to find a probability after a condition is already known. They should treat the given condition as the new sample space, then count how many of those outcomes also match the event in question. Tables, Venn diagrams, and two-way frequency tables are the main tools.
Mastery looks like choosing the right denominator every time and explaining the answer in context, not just writing a fraction. Students often get stuck by using the total sample space instead of the restricted group. They also mix up “A given B” and “B given A,” especially when the wording is long.
Ways to teach it
- Hands-on activity: Give students colored cards with two traits, such as shape and color, then have them physically sort the condition first.
- Discussion prompt: Ask, “If we only look at students who ride the bus, what does the denominator become, and why?”
- Quick assessment: Show a two-way table and ask students to compute one conditional probability and explain the denominator in one sentence.
- Real-world connection: Use a sports stat table to find the chance a player made a shot, given that it was a free throw.
Plan a lesson for CCSS.Math.Content.HSS-CP.B.6
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Related standards
- 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.7
Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of the model.
- CCSS.Math.Content.7.SP.C.7a
Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events.
- CCSS.Math.Content.HSS-CP.B.8
(+) Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.