Identify the distribution and provide a symbolic answer or an Excel expression.
ID: 3340768 • Letter: I
Question
Identify the distribution and provide a symbolic answer or an Excel expression.
A sequence of double-blind studies are carried out as for Problem X (not relevant to this problem), in which among the patients finishing the study, 38% were in the control group, 32% received Treatment 1, and 30% received treatment 2. Superior results were obtained by 8% of the placebo group, 28% of those receiving treatment 1, and 33% of those receiving treatment 2. If superior results were observed for a patient, what is the probability that he/she was receiving treatment 2?
Explanation / Answer
P(control group) = 0.38
P(treatment 1) = 0.32
P(treatment 2) = 0.3
P(superior results | control group) = 0.08
P(superior results | treatment 1) = 0.28
P(superior results | treatment 2) = 0.33
P(superior results) = P(superior results | control group) * P(control group) + P(superior results | treatment 1) * P(treatment 1) + P(superior results | treatment 2) * P(treatment 2)
= 0.08 * 0.38 + 0.28 * 0.32 + 0.33 * 0.3
= 0.219
P(treatment 2 | superior results) = P(superior results | treatment 2) * P(treatment 2) / P(superior results)
= 0.33 * 0.3 / 0.219
= 0.4521