Problem preview
S-CP.7 Warmup M2-069-A09-V01

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

The event that neither \(A\) nor \(B\) occurs is the complement of \(A~\text{or}~B\). Calculate \(1-0.72\).

Big Picture

What this problem is really about

Neither event means the complement of their inclusive union. We’ll translate the wording into that complement, subtract the known union probability from one, convert the remainder to a percent, and check that the event and its complement sum to the full probability.

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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