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Home » Use the Law of Total Probability to find \( P(F) \): - Veritas Home Health

Use the Law of Total Probability to find \( P(F) \): - Veritas Home Health

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A marine biologist reports that a genetically engineered coral species grows at a rate of 1.4 times per year, compared to 0.8 times for natural coral. If a reef starts with 200 mature fragments of each, what is the positive difference in population after 2 years?

📌 Engineered: \( 200 \times 1.4^2 = 200 \times 1.96 = 392 \)

📌 Natural: \( 200 \times 0.8^2 = 200 \times 0.64 = 128 \)

📌 Difference = 392 - 128 = 264

📌 The data analyst finds that reducing patient readmission rates in 8 clinics led to an average drop from 18% to 12%. If each clinic serves 250 patients annually, how many fewer readmissions occurred citywide due to this improvement?

📌 Reduction per clinic: \( 250 \times (0.18 - 0.12) = 250 \times 0.06 = 15 \)

📌 Total fewer readmissions = 8 × 15 = 120

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