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S-CP.5 Core M2-067-R02-V02

Explain conditional probability and independence in everyday language and situations.

Verify unchanged likelihood under independence

Problem

For \(\text{two}\) fair tosses, compare \(P(\text{second}~\text{heads})\) with \(P(\text{second}~\text{heads}~|~\text{first}~\text{heads})\) to decide independence.

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P(B|A) = 1/2, so the toss outcomes are independent.

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

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

P(A) = 1/2 and P(A|B) = 1/2, so the toss outcomes 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