In the tests of a new pharmaceutical product, data was collected for use in the approval process requied by the U.S. FDA. Some participants were given a placebo, an inert substance that looks like the drug; others were given the drug. The data is shown:

Question

In the tests of a new pharmaceutical product, data was collected for use in the approval process requied by the U.S. FDA. Some participants were given a placebo, an inert substance that looks like the drug; others were given the drug. The data is shown: 
          No Help        Help
   Drug      22            47
  Placebo    31            20
What is the probability that 
A) the participants perceived that their "medication" helped if they received the drug?
B) the participants perceived that their "medication" helped if they received placebo?
C) the participants perceived that their "medication" helped?

Answer: A) 47/69  68%   B) 20/51   39%   C) 67/53  14/53  59%

Is this correct?
Thanks.

PsyDAG · Answer

Notice that your answers to A and B sum to more than 100%. Is that possible? Your grand total is the sum of all the cells. A) 47/grand total B) 20/grand total C) 67/grand total

MathMate · Answer

(A) and (B) are correct.
I am not sure how your calculated (C).

Question (C) implies favorable results from all participants, namely 22+47+31+20=120.
The favorable results are 47+20=67.
So the percentages are: 67/120 = 56%.