A new cold medication was tested by giving 110 people the drug and 100 people a placebo. A control group consisted of 100 people who were given no treatment. The number of people in each group who showed improvement is shown in the table.   Use this information to solve parts​ (a) through​ (f) below.     Cold drug Placebo Control Total Improvement 70 55 20

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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A new cold medication was tested by giving 110 people the drug and 100 people a placebo. A control group consisted of 100 people who were given no treatment. The number of people in each group who showed improvement is shown in the table.
 
Use this information to solve parts​ (a) through​ (f) below.
 
 
Cold drug
Placebo
Control
Total
Improvement
70
55
20
145
No improvement
40
45
80
165
Total
110
100
100
310
 
 
a. What is the probability that a randomly selected person in the study was given the placebo or was in the control​ group?
 
The probability is ?
​(Round to the nearest thousandth as​ needed.)
 
b. What is the probability that a randomly selected person​ improved?
 
The probability is ?
​(Round to the nearest thousandth as​ needed.)
 
c. What is the probability that a randomly selected person was given the drug and​ improved?
 
The probability is ?
​(Round to the nearest thousandth as​ needed.)
 
d. What is the probability that a randomly selected person who improved was given the​ drug?
 
The probability is ?
​(Round to the nearest thousandth as​ needed.)
 
e. What is the probability that a randomly selected person who was given the drug​ improved?
 
The probability is ?
​(Round to the nearest thousandth as​ needed.)
 
f. Based on these​ data, does the drug appear to be​ effective? Explain.
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