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S-CP.2 Warmup M2-064-A03-V01

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

Decide whether two events are independent by comparing P(A and B) with P(A)P(B)

Problem

Using the diagram's counts, test independence by comparing \(20/100\) with \((40/100)(50/100)\). State whether the probabilities are equal.

Two-way-table facts: total 100, A count 40, B count 50, and A-and-B count 20. Open full size
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What this problem is really about

Counts must first be normalized by the common total before independence is tested. We’ll convert the two event counts and overlap count to probabilities, multiply the marginals, reduce both sides to the same value, and classify the events from the exact probability comparison.

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Four variants of this problem type
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 two events are independent by comparing P(A and B) with P(A)P(B)