Explanation Given: The probability of mortality rate of a certain disease is 0.35 . The probability of recovered rate of a certain disease is 0.65 . The total number of patients who are given this drug is 12 The total number of patients who recovered is 9 . Approach: The probability of getting exactly r successes in n independent trials of an experiment is, P ( r succeses in n trials ) = C ( n , r ) p r ( 1 − p ) n − r … ( 1 ) Here, p is the probability of success in one trial and 1 − p is the probability of failure in one trial. Calculation: The probability that nine or more patients would have recovered without the drug includes the cases in which the 9 patients would have recovered without the drug, 10 patients would have recovered without the drug, 11 patients would have recovered without the drug, and 12 patients would have recovered without the drug. Substitute 12 for n , 9 for r , and 0.65 for p in equation ( 1 ) . Thus, P ( E ) = [ C ( 12 , 9 ) ( 0.65 ) 9 ( 0.35 ) 12 − 9 + C ( 12 , 10 ) ( 0.65 ) 10 ( 0.35 ) 12 − 10 + C ( 12 , 11 ) ( 0.65 ) 11 ( 0.35 ) 12 − 11 + C ( 12 , 12 ) ( 0 To determine (b) To find: Whether the drug appears to be effective.

Algebra and Trigonometry (MindTap Course List)

4th Edition

ISBN: 9781305071742

Author: James Stewart, Lothar Redlin, Saleem Watson

Publisher: Cengage Learning

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Chapter 14.CR, Problem 45E

To determine

(a)

To find:

The probability that nine or more patients would have recovered without the drug.

To determine

(b)

To find:

Whether the drug appears to be effective.

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Chapter 14.CR, Problem 44E

Chapter 14.CR, Problem 46E

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Algebra and Trigonometry (MindTap Course List)

Ch. 14.1 - CONCEPTS The Fundamental Counting Principle says...Ch. 14.1 - CONCEPTS The number of ways of arranging r objects...Ch. 14.1 - Prob. 3E Ch. 14.1 - Prob. 4E Ch. 14.1 - Prob. 5E Ch. 14.1 - Prob. 6E Ch. 14.1 - Prob. 7E Ch. 14.1 - Prob. 8E Ch. 14.1 - Prob. 9E Ch. 14.1 - Prob. 10E

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(a) To find: The probability that nine or more patients would have recovered without the drug.

Solution Summary: The author calculates the probability that nine or more patients would have recovered without the drug.