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.

To find the probability of receiving a placebo and reporting an improvement, we need to follow a step-by-step process.

Step 1: Draw a Tree Diagram
Start by drawing a tree diagram to visualize the different outcomes. Write "Medication A" at the beginning of one branch and "Placebo" at the beginning of the other branch.

Step 2: Assign Probabilities
Assign probabilities to each branch based on the given information. The probability of receiving Medication A is 80%, so write 0.8 on the branch for Medication A. The probability of receiving a placebo is the complement of the probability of receiving Medication A, which is 100% - 80% = 20%. So, write 0.2 on the branch for the Placebo.

Step 3: Add More Branches
Continue extending each branch to represent the different outcomes. On the Medication A branch, write 0.76 on the branch for improvement since 76% reported an improvement. Write 0.24 on the branch for no improvement since it is the complement (100% - 76% = 24%).

On the Placebo branch, write 0.62 for no improvement since 62% reported no improvement. To find the probability of improvement for the Placebo group, subtract the probability of no improvement from 1 (100% - 62% = 38%). So, write 0.38 on the branch for improvement.

Step 4: Calculate the Probability of Placebo and Improvement
To find the probability of receiving a placebo and reporting an improvement, multiply the probabilities along the corresponding branches. So, 0.2 (probability of placebo) multiplied by 0.38 (probability of improvement for placebo) equals 0.076.

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

The answer would be .076%