Problem preview

S-CP.2 Warmup M2-064-A09-V03

Determine event independence using P(A and B)=P(A)P(B).

Decide whether a probability context suggests independent events and confirm with P(A and B)=P(A)P(B)

Problem

Before calculating, does this context suggest independence: randomly selecting \(\text{two}~\text{students}\) with replacement from the same list?

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No, these events seem dependent because once one student is picked, that result is already part of the experiment.

Yes, these events seem independent because replacing the first student puts the full list back for the second pick.

Yes, these events seem independent because selecting two students always means each pick has nothing to do with the other.

No, these events seem dependent because the two students are chosen from the same list, so the picks must affect each other.

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Curriculum context

Course: Math II
Standard: S-CP.2
Category: Statistics and Probability
Domain: Conditional Probability and the Rules of Probability
Objective: Determine event independence using P(A and B)=P(A)P(B).
Problem type: Decide whether a probability context suggests independent events and confirm with P(A and B)=P(A)P(B)