CCSS.Math.Content.HSS-CP.A.3
The standard
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 given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
Common Core State Standards for Mathematics
What this standard means
Students need to read two-way tables, tree diagrams, or simple situations and find the chance of one event when another event is already known. They should connect “given” to limiting the sample space, not to multiplying by the second event.
Mastery looks like choosing the right denominator, explaining the answer in context, and deciding whether two events are independent by comparing probabilities. Students often use the total sample size when they should use only the known group. They also mix up “and” with “given.”
Ways to teach it
- Give students a two-way table of students by grade and club membership, then have them physically cover rows or columns to show the given group.
- Ask students to write one sentence explaining the difference between “student is a senior and in band” and “student is in band given senior.”
- Use an exit ticket with one two-way table and ask for P(A), P(A given B), and whether A and B are independent.
- Use a sports shot chart and ask whether a player’s chance of scoring changes when the shot is from the corner.
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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.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.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.
- 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...