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%.