The probability is 0.4 that the final exam is difficult. If the final exam is difficult, the probability is 0.3 that Nancy will pass the course. If the final exam is not difficult, the probability is 0.9 that Nancy will pass the course.   Based on this body of information, answer the following questions.   (A) What is the probability that the final exam is not difficult? (B) What is the probability that the final exam is difficult AND Nancy will pass the course? [Use the multiplication rule.] (C) What is the probability that the final exam is not difficult AND Nancy will pass the course? [Use the multiplication rule.]

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter8: Sequences, Series,and Probability
Section8.7: Probability
Problem 50E: Flexible Work Hours In a recent survey, people were asked whether they would prefer to work flexible...
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  1. The probability is 0.4 that the final exam is difficult.
  2. If the final exam is difficult, the probability is 0.3 that Nancy will pass the course.
  3. If the final exam is not difficult, the probability is 0.9 that Nancy will pass the course.
 
Based on this body of information, answer the following questions.
 
(A) What is the probability that the final exam is not difficult?
(B) What is the probability that the final exam is difficult AND Nancy will pass the course? [Use the multiplication rule.]
(C) What is the probability that the final exam is not difficult AND Nancy will pass the course? [Use the multiplication rule.]
(D) What is the probability that Nancy will pass the course? [Use additivity from (B) and (C).]
(E) Given the observation that Nancy passed the course, what is the probability that the final exam was difficult? [Use Bayes’ Theorem.]
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