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.

Question

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

To find P(placebo and improvement), we need to first find the probability of receiving a placebo and then the probability of reporting an improvement if receiving a placebo.

P(placebo) = 1 - P(medication A) = 1 - 0.80 = 0.20

P(no improvement | placebo) = 0.62

P(improvement | placebo) = 1 - P(no improvement | placebo) = 1 - 0.62 = 0.38

Now, we can find P(placebo and improvement) using the formula for conditional probability:

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

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