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Home » 🚨 You Won’t Believe What a Cursement Can Do in 7 Seconds! - SUpost

🚨 You Won’t Believe What a Cursement Can Do in 7 Seconds! - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 5Question: A materials scientist is testing a composite material with 5 microscopic cracks, each independently healed with probability $ \frac{1}{3} $. What is the probability that exactly 2 cracks are healed?

📌 Solution: The probability follows a binomial distribution with parameters $ n = 5 $ and $ p = \frac{1}{3} $. The probability of exactly 2 successes is $ \binom{5}{2} \left(\frac{1}{3}\right)^2 \left(\frac{2}{3}\right)^3 $. Calculating:

📌 \binom{5}{2} = 10, \quad \left(\frac{1}{3}\right)^2 = \frac{1}{9}, \quad \left(\frac{2}{3}\right)^3 = \frac{8}{27}.

📌 Multiplying: $ 10 \cdot \frac{1}{9} \cdot \frac{8}{27} = \frac{80}{243} $.

📌 \boxed{\dfrac{80}{243}}

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