Participants 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. show all work

Question

Participants 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. show all work

Answer 1

Let's break this down step by step:

1. Probability of receiving placebo: 20% (100% - 80%)

2. Probability of improvement given medication A: 76%

3. Probability of no improvement given placebo: 62%

Now, we need to find the probability of receiving placebo and improvement.

P(placebo and improvement) = P(placebo) * P(improvement given placebo)

P(placebo) = 20%
P(no improvement given placebo) = 1 - 0.62 = 0.38

P(placebo and improvement) = 0.20 * 0.38
P(placebo and improvement) = 0.076

Therefore, the probability of receiving a placebo and reporting improvement is 0.076 or 7.6%.