A paper described the results of a medical study in which one treatment was shown to be better for men
and better for women than a competing treatment. However, if the data for men and women are combined,
it appears as though the competing treatment is better.
To see how this can happen, consider the accompanying data tables constructed from information in the
paper. Subjects in the study were given either Treatment A or Treatment B, and their survival was noted.
Let S be the event that a patient selected at random survives, A be the event that a patient selected at
random received Treatment A, and B be the event that a patient selected at random received Treatment B.
(Round your answers to three decimal places.)
(a) The following table summarizes data for men and women combined
Survived Died Total
Treatment A 216 84 300
Treatment B 241 59 300
Total 457 143
(i) Find P(S)
(ii) Find P(S|A)
(iii) Find P(S|B)
(iv) Which treatment appears to be better?
Treatment A
Treatment B
Guide On Rating System
Vote
(i) P(S) = (Number of patients who survived) / (Total number of patients)
P(S) = (457) / (600) = 0.762
(ii) P(S|A) = (Number of patients who received Treatment A and survived) / (Total number of patients who received Treatment A)
P(S|A) = (216) / (300) = 0.720
(iii) P(S|B) = (Number of patients who received Treatment B and survived) / (Total number of patients who received Treatment B)
P(S|B) = (241) / (300) = 0.803
(iv) Since P(S|B) > P(S|A), Treatment B appears to be better.
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