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Home » To find where $ C(t) $ is increasing, we solve: - Midis

To find where $ C(t) $ is increasing, we solve: - Midis

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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📌 Multiply all parts:

📌 \cdot 0.0625 \cdot 0.421875 = 0.626953125

📌 \boxed{0.626953125}

📌 Question: An AI system classifies 7 independent data points into two categories — success or failure — each with a 40% chance of success. What is the probability that at least 5 of the classifications are successes?

📌 Solution: This is a binomial probability problem with $ n = 7 $, $ p = 0.4 $, and we want $ P(X \geq 5) = P(X=5) + P(X=6) + P(X=7) $.

📌 Using the binomial formula:

📌 $ 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 $

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