Answer the questions that follow based on the data in the chart. The cholesterol
ID: 3126082 • Letter: A
Question
Answer the questions that follow based on the data in the chart. The cholesterol reducing drug Lipitor consists of atorvastatin.
10 mg Atorvastatin Placebo
Headache 15 65
No headache 17 3
1). If 1 of the 100 subjects is randomly selected, find the probability of getting someone who did not have a headache.
2). If 1 of the 100 subjects is randomly selected, find the probability of getting someone who was not treated with 10 mg of atorvastatin.
3). If 1 of the 100 subjects is randomly selected, find the probability of getting someone who was given a placebo or did have a headache.
4). If two different subjects are randomly selected, find the probability that they both have a headache.
5). If one subject is randomly selected, find the probability that the subject had a headache, given that the subject was given the placebo.
Explanation / Answer
Let
H = headace
A = treated with Atorvastatin
P = placebo
1.
P(H') = (17+3)/100 = 0.20 [ANSWER]
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2.
P(P) = (65+3)/100 = 0.68 [ANSWER]
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3.
P(P U H) = (65+3+15)/100 = 0.83 [ANSWER]
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4.
There are 80 who have headache.
Note that the probability of x successes out of n trials is
P(x) = C(N-K, n-x) C(K, x) / C(N, n)
where
N = population size = 100
K = number of successes in the population = 80
n = sample size = 2
x = number of successes in the sample = 2
Thus,
P( 2 ) = 0.638383838 [ANSWER]
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5.
P(H|P) = 65/(65+3) = 0.955882353 [ANSWER]
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