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Home » Windows Powershell For Loop: The Ultimate Shortcut Hidden from Most Users! - Redraw

Windows Powershell For Loop: The Ultimate Shortcut Hidden from Most Users! - Redraw

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 Given $\cos \theta = \frac{1}{3}$, compute:

📌 \tan \theta = \frac{\sqrt{1 - \left(\frac{1}{3}\right)^2}}{\frac{1}{3}} = \frac{\sqrt{1 - \frac{1}{9}}}{\frac{1}{3}} = \frac{\sqrt{\frac{8}{9}}}{\frac{1}{3}} = \frac{\frac{2\sqrt{2}}{3}}{\frac{1}{3}} = 2\sqrt{2}

📌 $$Question: A venture capitalist invests in 5 startups, each with a 25% chance of success independently. What is the probability that exactly 2 of the startups succeed?

📌 Solution: We model this as a binomial probability problem. The probability of exactly $ k $ successes in $ n $ independent trials, each with success probability $ p $, is given by:

📌 P(k; n, p) = \binom{n}{k} p^k (1-p)^{n-k}

📌 Here, $ n = 5 $, $ k = 2 $, and $ p = 0.25 $. Then:

📌 P(2; 5, 0.25) = \binom{5}{2} (0.25)^2 (0.75)^3

📌 First, compute the binomial coefficient:

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