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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 P(placebo and improvement), we can break it down into two parts: P(placebo) and P(improvement | placebo).
1. P(placebo) = 100% - 80% = 20%
2. P(improvement | placebo) = 100% - 62% = 38%
3. P(placebo and improvement) = P(placebo) * P(improvement | placebo)
= 20% * 38%
= 0.20 * 0.38
= 0.076
Therefore, P(placebo and improvement) is 0.076 or 7.6%.