AP Statistics 2.6 Conditional Probability Questions

Practise restricting sample spaces, connecting conditional and joint probabilities, applying multiplication rules, and reversing conditions through total probability.

Exam points

restrict the sample space to the given event and calculate the requested conditional proportion
connect conditional and joint probabilities through the intersection-over-given-event formula
apply the general multiplication rule to intersections and ordered sequences of events
use total probability and joint components to calculate a condition in the reverse direction

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.

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

Question 1