Question

For a study on a new cold medicine, a group of 100 participants with cold symptoms was studied for one month in the spring. One-fifth of the participants were given the cold medicine, and the rest of the participants were given a placebo, a pill that has no active ingredients. Of the participants that were given the medicine, 70% felt improvement of their symptoms. Of the participants that were given the placebo, 80% felt improvement of their symptoms. What is the probability of randomly choosing a participant who took the placebo, given they did not feel improvement?

Answer 1

One fifth given medicine= 20 people
Placebo therefore= 80 people

Of the ones given medicine 70% (14 people) felt inprovement/ 30% did not (6 people)

Of the placebo group 80% felt improvement (64 people)/ 20% did not (16 people).

You are given that the person chosen felt no improvement so 6+16=22.
Of the 22 the chance of choosing someone from the placebo group is 16...
16/22= 8/11