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?