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 of the participants is 1/5*100=100/5=20 is the number of the participants given medicine. So the number of participants given placebo is 100-20=80.

80% of the 80 who took placebo felt improvements, so 20% of 80, which is
(20/100)*80=(2/10)*80=160/10=16 is the number of participants who took placebo and felt no improvement.

P(choosing participant who took placebo and felt no improvement)=

n(participant who took placebo and felt no improvement)/n(participants)
=16/100=0.16