Question

Participants in a study of a new medication A or a placebo. Find P (placebo and improvement). You may find it helpful to make a tree diagram of the problem.
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

The tree diagram is constructed and attached as an image below.

80% of the participants received medication, this means 20% received placebo. Among those who received medication, 76% reported improvement, this means rest 24% reported no improvement. Among those who received Placebo, 62% reported no improvement, this means rest 38% reported improvement.

The probability of P(Placebo and Improvement) will be = 20% x 38%
P(Placebo and Improvement) = 0.20 x 0.38 = 0.076 = 7.6%

This means there is 7.6% probability that those who received Placebo reported Improvement.