A new cold medication was tested by giving 120 people the drug and 100 people a

Question

A new cold medication was tested by giving 120 people the drug and 100 people a placebo. A control group consisted of 120 people who were given no treatment. The number of people in each group who showed improvement is shown in the table below.  

Cold Drug   Placebo   Control   Total

Improvement 70 55 40 165 No Improvement 50 45 80 175 Total 120 100 120 340

a) What is the probability that a randomly selected person in the study either was given the placebo or was in the control group? ____________

b) What is the probability that a randomly selected person either was given the drug or improved? _____________

c) What is the probability that a randomly selected person was given the drug and improved? ______________

d) What is the probability that a randomly selected person who improved was given the drug? ________

e) What is the probability that a randomly selected person who was given the drug improved? ________

f) Based on these data, does the drug appear to be effective? ____________

Explanation / Answer

Let

CD = cold drug
P = placebo
C = control
I = improved
NI = no improvement

a)
From the table,

P(P U C) = (100+120)/340 = 0.647058824 [ANSWER]

**************************

b)
From the table,

P(CD U I) = (70+50+55+40)/340 = 0.632352941 [ANSWER]

*************************

c)

From the table,

P(CD n I) = 70/340 = 0.205882353 [ANSWER]

*************************

d)

From the table,

P(CD|I) = 70/165 = 0.424242424 [ANSWER]

*************************

e)

From the table,

P(I|CD) = 70/120 = 0.583333333 [ANSWER]

**************************

f)

As

P(I) = 165/340 = 0.485294118

P(I|CD) = 0.5833333333

As P(I|CD) > P(I), yes, it appears to be effective. [ANSWER]

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