Problem preview
S-CP.5 Core M2-067-R10-V01

Explain conditional probability and independence in everyday language and situations.

Distinguish a conditional probability from its reverse

Problem

Using the test table, calculate \(P(T+|C)=90/100\) and \(P(C|T+)=90/135\) with their different conditioned totals. Reduce and compare.

Big Picture

What this problem is really about

Reversed conditionals share the same overlap numerator but use different conditioned totals. We’ll compute the test-positive rate within the condition row, reverse the direction and use the positive-test column, reduce both fractions, and compare their distinct meanings and values.

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Four variants of this problem type
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
Distinguish a conditional probability from its reverse