AP Statistics 2.6 Conditional Probability Overview

Calculate conditional probabilities by restricting the sample space, using intersections, and connecting joint and conditional probabilities.

Covered syllabus points

2.6.A—Calculate conditional probabilities

A medical researcher surveyed a large group of men and women about whether they take medicine as prescribed. The responses were categorized as never, sometimes, or always. The relative frequency of each category is shown in the table.

	Never	Sometimes	Always	Total
Men	0.0564	0.2016	0.2120	0.4700
Women	0.0636	0.1384	0.3280	0.5300
Total	0.1200	0.3400	0.5400	1.0000

One person from those surveyed will be selected at random.

What is the probability that the person selected will be someone whose response is never given that the person is a woman?

P( never $\mid$ woman $)=\frac{P(\text { never and woman })}{P(\text { woman })}=\frac{0.0636}{0.53}=0.12$

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Covered syllabus points

2.6 Conditional Probability question 1