Problem preview

S-CP.5 Core M2-067-R02-V03

Explain conditional probability and independence in everyday language and situations.

Verify unchanged likelihood under independence

Problem

After replacement and shuffling, compare \(P(\text{second}~\text{red})\) with \(P(\text{second}~\text{red}~|~\text{first}~\text{ace})\) and classify the two draw events.

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P(B|A) = 1/2, so A and B are independent.

P(A) = 1/2 and P(A|B) = 1/2 after replacement, so A and B are independent.

P(A) = 1/3 and P(A|B) = 1/2, so A and B are independent.

P(A) = 1/2 and P(A|B) = 1/2, so A and B are dependent.

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Curriculum context

Course: Math II
Standard: S-CP.5
Category: Statistics and Probability
Domain: Conditional Probability and the Rules of Probability
Objective: Explain conditional probability and independence in everyday language and situations.
Problem type: Verify unchanged likelihood under independence