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 didn't improve and they received the non-placebo and identify the type of probability found. 

• A. 0.4; Joint probability
• B. 0.4; Conditional probability
• C. 0.2; Joint probability
• D. 0.2; Conditional probability

Answer: (C)

Verified step by step guidance

1. Step 1: Understand the problem. We are tasked with finding the probability that a person's symptoms didn't improve and they received the non-placebo. This is a joint probability, as it involves the intersection of two events: 'Not Improved' and 'Non-Placebo'.
2. Step 2: Locate the relevant data in the table. From the table, the number of people whose symptoms didn't improve and who received the non-placebo is 20. The total number of participants in the trial is 100.
3. Step 3: Recall the formula for joint probability. Joint probability is calculated as the number of favorable outcomes divided by the total number of outcomes. In this case, the favorable outcome is the count of people who didn't improve and received the non-placebo.
4. Step 4: Write the formula using MathML: $\frac{20}{100}$. This represents the probability of the joint event.
5. Step 5: Interpret the type of probability. Since we are calculating the probability of two events occurring together ('Not Improved' and 'Non-Placebo'), this is classified as a joint probability.