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S-CP.7 Warmup M2-069-A09-V03

Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).

Find the probability that neither event occurs using the Addition Rule and the complement

Problem

In the Venn diagram, the \(20\) outcomes outside both circles represent neither event. Divide \(20\) by the total \(12+8+10+20\) and reduce.

Prompt Venn diagram: A-only is 12, the overlap is 8, B-only is 10, and 20 outcomes are outside both events, for 50 outcomes total. Find P(neither A nor B); the result is withheld. Open full size
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Four variants of this problem type
Curriculum context
Course
Math II
Standard
S-CP.7
Category
Statistics and Probability
Domain
Conditional Probability and the Rules of Probability
Objective
Apply and interpret the Addition Rule P(A or B)=P(A)+P(B)-P(A and B).
Problem type
Find the probability that neither event occurs using the Addition Rule and the complement