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hampton inn austin east side 5th street - Feedz API

📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 So, the probability of drawing exactly two red marbles is $\boxed{\dfrac{189}{455}}$

📌 Question: If I roll a fair six-sided die four times, what is the probability that I roll the number 4 exactly twice?

📌 Solution: This is a binomial probability problem with $ n = 4 $ trials (rolls), success probability $ p = \frac{1}{6} $ (rolling a 4), and we want exactly $ k = 2 $ successes.

📌 The binomial probability formula is:

📌 P(k) = \binom{n}{k} p^k (1-p)^{n-k}

📌 Substitute values:

📌 P(2) = \binom{4}{2} \left(\frac{1}{6}\right)^2 \left(\frac{5}{6}\right)^2

📌 \binom{4}{2} = 6, \quad \left(\frac{1}{6}\right)^2 = \frac{1}{36}, \quad \left(\frac{5}{6}\right)^2 = \frac{25}{36}

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