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, categorizing participants into two groups: Placebo and Non-Placebo. Each group is further divided into 'Improved' and 'Not Improved' symptoms, with totals provided for each category.
2. Step 2: Define Marginal Probability. Marginal probability refers to the probability of a single event occurring, irrespective of other events. In this case, it would be the probability of 'Improved' symptoms across all participants.
3. Step 3: Calculate the Marginal Probability of 'Improved' symptoms. To find this, divide the total number of participants with 'Improved' symptoms (40) by the overall total number of participants (100). Use the formula: P(Improved) = Total Improved / Grand Total.
4. Step 4: Define Joint Probability. Joint probability refers to the probability of two events occurring simultaneously. For example, the probability that a participant is in the Non-Placebo group and their symptoms improved.
5. Step 5: Calculate the Joint Probability for 'Improved' symptoms in the Non-Placebo group. To find this, divide the number of participants in the Non-Placebo group with 'Improved' symptoms (30) by the overall total number of participants (100). Use the formula: P(Improved and Non-Placebo) = Non-Placebo Improved / Grand Total.