Answered: ther data. (a) How many people got…

College Algebra

1st Edition

ISBN:9781938168383

Author:Jay Abramson

Publisher:Jay Abramson

Chapter9: Sequences, Probability And Counting Theory

Section9.7: Probability

Problem 2SE: What is a sample space?

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Question

A study was done to determine the efficacy of three different drugs—A, B, and C—in relieving headache pain. Over the period covered by the study, 50 subjects were given the chance to use all three drugs. The following results were obtained.

20 reported relief from drug A
20 reported relief from drug B
30 reported relief from drug C
8 reported relief from both drugs A and B
13 reported relief from both drugs A and C
14 reported relief from both drugs B and C
42 reported relief from at least one of the drugs

Note that some of the 20 subjects who reported relief from drug A may also have reported relief from drugs B or C. A similar occurrence may be true for the other data.

(a) How many people got relief from none of the drugs?

(b) How many people got relief from all three drugs?

(c) Let A be the set of all subjects who got relief from drug A, B the set of all subjects who got relief from drug B, and C the set of all subjects who got relief from drug C. Fill in the numbers for all eight regions of the following diagram.

(d) How many subjects got relief from drug A only?