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Home » The projection of $\mathbfp$ onto $\mathbfq$ is given by: - Moon Smoking

The projection of $\mathbfp$ onto $\mathbfq$ is given by: - Moon Smoking

📅 May 15, 2026 👤 scraface

May 15, 2026

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📌 \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 $

📌 $ P(1) = \binom{6}{1} (0.3)^1 (0.7)^5 = 6 \cdot 0.3 \cdot 0.16807 = 0.302526 $

📌 $ P(2) = \binom{6}{2} (0.3)^2 (0.7)^4 = 15 \cdot 0.09 \cdot 0.2401 = 0.324135 $

📌 P(X < 3) = 0.117649 + 0.302526 + 0.324135 = 0.74431

📌 \boxed{0.74431}

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