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Home » 5: The Absolute Difference Between Aluminum and Aluminium That Will Surprise You! - Abbey Badges

5: The Absolute Difference Between Aluminum and Aluminium That Will Surprise You! - Abbey Badges

📅 February 26, 2026 👤 scraface

Feb 26, 2026

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📌 $ P(5) = \binom{7}{5} (0.4)^5 (0.6)^2 = 21 \cdot 0.01024 \cdot 0.36 = 0.0774144 $

📌 $ P(6) = \binom{7}{6} (0.4)^6 (0.6)^1 = 7 \cdot 0.004096 \cdot 0.6 = 0.0172032 $

📌 $ P(7) = \binom{7}{7} (0.4)^7 (0.6)^0 = 1 \cdot 0.0016384 \cdot 1 = 0.0016384 $

📌 P(X \geq 5) = 0.0774144 + 0.0172032 + 0.0016384 = 0.096256

📌 \boxed{0.096256}

📌 Question: A chemical engineer tests 6 independent algae samples for biofuel yield, each with a 30% chance of producing high yield. What is the probability that fewer than 3 samples produce high yield?

📌 Solution: This is a binomial probability problem with $ n = 6 $, $ p = 0.3 $, and we want $ P(X < 3) = P(X=0) + P(X=1) + P(X=2) $.

📌 $ P(0) = \binom{6}{0} (0.3)^0 (0.7)^6 = 1 \cdot 1 \cdot 0.117649 = 0.117649 $

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