4. Probability
Introduction to Contingency Tables
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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, given that they received the placebo and identify the type of probability found.
A
0.1; Marginal probability
B
0.1; Conditional probability
C
0.2; Conditional probability
D
0.2; Marginal probability
Verified step by step guidance1
Step 1: Understand the problem. We are tasked with finding the probability that a person's symptoms improved, given that they received the placebo. This is a conditional probability problem, where we focus on the subset of individuals who received the placebo.
Step 2: Recall the formula for conditional probability. The conditional probability P(A|B) is calculated as P(A ∩ B) / P(B), where A is the event 'symptoms improved' and B is the event 'received placebo'.
Step 3: Identify the relevant values from the table. From the table, the number of people who received the placebo and whose symptoms improved is 10. The total number of people who received the placebo is 50.
Step 4: Apply the formula for conditional probability. Substitute the values into the formula: P(improved | placebo) = (number of improved and placebo) / (total number of placebo). This simplifies to P(improved | placebo) = 10 / 50.
Step 5: Interpret the type of probability. Since we are calculating the probability of an event (symptoms improved) within a specific subset (placebo group), this is a conditional probability.
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