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.

Answer 1

Notice that your answers to A and B sum to more than 100%. Is that possible?

Your grand total is the sum of <I>all</I> the cells.

A) 47/grand total
B) 20/grand total
C) 67/grand total

Answer 2

(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%.