The table below shows the results from a drug trial for a new ADHD medication. Use the table to find the probability that a person's symptoms improved and identify the type of probability found.

• A. 0.8; Marginal Probability
• B. 0.8; Joint Probability
• C. 0.4; Joint Probability
• D. 0.4; Marginal Probability

Answer: (D)

Verified step by step guidance

1. Step 1: Understand the table. The table provides data on the results of a drug trial for a new ADHD medication. It categorizes participants into two groups: Placebo and Non-Placebo, and further divides them based on whether their symptoms improved or not.
2. Step 2: Define marginal probability. Marginal probability refers to the probability of a single event occurring, regardless of other variables. In this case, we are looking for the probability that a person's symptoms improved, regardless of whether they were in the Placebo or Non-Placebo group.
3. Step 3: Calculate the marginal probability. To find the marginal probability of symptoms improving, divide the total number of participants whose symptoms improved (found in the 'Improved' row under the 'Total' column) by the overall total number of participants (found in the 'Total' row under the 'Total' column). Use the formula: P(Improved) = Total Improved / Grand Total.
4. Step 4: Interpret the result. The marginal probability calculated represents the likelihood that a randomly selected participant from the study experienced an improvement in symptoms, regardless of the group they were in.
5. Step 5: Compare with the given answer. The problem states that the correct answer is 0.4; Marginal Probability. Verify that this matches the calculation from Step 3 and confirm the type of probability as marginal.