Question

show all the stepsParticipants in a study of a new medication received either medication A or a placebo. Find P(placebo and improvement). You may find it helpful to make a tree diagram of the problem on a separate piece of paper.Of all those who participated in the study, 80% received medication A. Of those who received medication A, 76% reported an improvement. Of those who received the placebo, 62% reported no improvement.

Answer 1

Tree Diagram

Of all the participants in the study, 80% received medication A (M) and 20% received the placebo (P).

The first branches of the tree diagram are:

Of those who received the placebo, 62% reported no improvement (NI), thus 38% reported improvement (I). We complete the lower branch with this information. The upper branch is not important for this question.

We want to calculate the probability of randomly selecting a participant that received a placebo and reported improvement.

We take the bottom path and determine the probability:

P = 20% × 38%

P = 0.20% × 0.38

P = 0.076

P = 7.6%