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?

Question

Barbara Delgado

Mathematics

31 October, 13:09

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?

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Robert Herman · 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