Problem preview

S-CP.8 Warmup M2-070-A08-V03

Apply and interpret the general Multiplication Rule with conditional probability.

Compare matched independent and dependent joint probabilities

Problem

Multiply \(0.10\times~0.10\) for independent failures and \(0.10\times~0.80\) for shared-supply failures, then compare the both-fail probabilities.

Answer choices

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Independent both-fail: 0.01. Shared-supply both-fail: 0.08. The independent probability is greater.

Add the factors: the independent case gives 0.20, and the shared-supply case gives 0.90.

Independent both-fail: 0.01. Shared-supply both-fail: 0.01. The probabilities are equal.

Independent both-fail: 0.01. Shared-supply both-fail: 0.08. The dependent probability is greater.

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Curriculum context

Course: Math II
Standard: S-CP.8
Category: Statistics and Probability
Domain: Conditional Probability and the Rules of Probability
Objective: Apply and interpret the general Multiplication Rule with conditional probability.
Problem type: Compare matched independent and dependent joint probabilities