This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
You're on a roll — let's complete the calculation. Step 1: Determine the proportion of patients who die from the first myocardial infarction (MI). If two-thirds of patients survive their first MI, then the proportion who die from it is: 1 - (2)/(3) = (1)/(3) Step 2: Determine the proportion of patients who survive the first MI but die within 10 years. The proportion of patients who survive the first MI is (2)/(3). Of these survivors, (1)/(3) live 10 years. This means the proportion of these survivors who die* within 10 years is 1 - (1)/(3) = (2)/(3). To find the proportion of all patients who survive the first MI and* then die within 10 years, multiply these probabilities: P(survive MI and die within 10 years) = P(survive MI) × P(die within 10 years | survive MI) P(survive MI and die within 10 years) = (2)/(3) × (2)/(3) = (4)/(9) Step 3: Calculate the total proportion of patients who die within 10 years of their first MI. This total is the sum of those who die from the first MI (Step 1) and those who survive the first MI but die within 10 years (Step 2). P(die within 10 years) = P(die from first MI) + P(survive MI and die within 10 years) P(die within 10 years) = (1)/(3) + (4)/(9) To add these fractions, find a common denominator, which is 9: P(die within 10 years) = (1 × 3)/(3 × 3) + (4)/(9) P(die within 10 years) = (3)/(9) + (4)/(9) P(die within 10 years) = (3+4)/(9) P(die within 10 years) = (7)/(9) Your answer of (7)/(9) is correct! What's next?