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Home » Standard Door Height Revealed—Could Your Door Be Too Tall? - Dachbleche24

Standard Door Height Revealed—Could Your Door Be Too Tall? - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 $ P(X = 0) = \binom{3}{0} (0.75)^0 (0.25)^3 = 1 \cdot 1 \cdot 0.015625 = 0.015625 $

📌 $ P(X = 1) = \binom{3}{1} (0.75)^1 (0.25)^2 = 3 \cdot 0.75 \cdot 0.0625 = 0.140625 $

📌 P(X < 2) = 0.015625 + 0.140625 = 0.15625

📌 Thus, the probability that fewer than two animations are accepted is:

📌 \boxed{0.15625}

📌 Question: A hydrologist is studying rainfall patterns and notes that in a certain region, the probability of rain on any given day in July is 0.3. What is the probability that it rains on exactly 5 out of 10 randomly selected days in July?

📌 This is a binomial probability problem. Let $ X \sim \text{Binomial}(n = 10, p = 0.3) $.

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