14....Mutually exclusive.....means that two things cannot happen simultaneously....so....you can't roll a 3 and a 4 at the same time...
P(placebo and improvement) = \(\frac{\text{number who received placebo and reported improvement}}{\text{total number who participated in the study}}\)
Let the total number of people who participated in the study = t
80% of those who participated in the study received med A . So…
20% of those who participated in the study received a placebo.
number of those who received the placebo = 0.2t
62% of those who received the placebo reported no improvement. So…
38% of those who received the placebo reported improvement.
number who received placebo and reported improvement = 0.38( 0.2t )
P(placebo and improvement) = \(\frac{0.38(0.2t)}{t}\) = 0.38(0.2) = 0.076 = 7.6%