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
This problem asks for the probability of contracting either glaucoma or diabetes. This is a classic application of the formula for the probability of the union of two events. Let G be the event of contracting glaucoma. Let D be the event of contracting diabetes. We are given the following probabilities: The lifetime probability of contracting glaucoma: P(G) = 0.02 The lifetime probability of contracting diabetes: P(D) = 0.025 The probability of contracting both diseases: P(G D) = 0.0008 To find the probability of contracting either glaucoma or diabetes, we use the formula for the union of two events: P(G D) = P(G) + P(D) - P(G D) Step 1: Substitute the given values into the formula. P(G D) = 0.02 + 0.025 - 0.0008 Step 2: Perform the addition. 0.02 + 0.025 = 0.045 Step 3: Perform the subtraction. P(G D) = 0.045 - 0.0008 P(G D) = 0.0442 The lifetime probability of contracting either glaucoma or diabetes is 0.0442. Comparing this result with the given options: a) 0.0442 b) 0.0392 c) 0.0458 d) 0.0492 Our calculated value matches option (a). The final answer is a) 0.0442. That's the last one for today! Send me the next one 📸