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Home » Set equal: 5 + 1.2d = 3 + 1.5d - Get link 4share

Set equal: 5 + 1.2d = 3 + 1.5d - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 $$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:

📌 \binom{5}{2} = \frac{5!}{2!(5-2)!} = \frac{120}{2 \cdot 6} = 10

📌 Now compute the powers:

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