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Home » The Ultimate Curated Collection of Sleep Stories to Transform Your Nights! - High Altitude Science

The Ultimate Curated Collection of Sleep Stories to Transform Your Nights! - High Altitude Science

📅 March 11, 2026 👤 scraface

Mar 11, 2026

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Question: If I roll a fair six-sided die four times, what is the proba...
Solution: This is a binomial probability problem with $ n = 4 $ trials...
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...
\binom{4}{2} = 6, \quad \left(\frac{1}{6}\right)^2 = \frac{1}{36}, \qu...
So:
P(2) = 6 \times \frac{1}{36} \times \frac{25}{36} = \frac{150}{1296} =...
Thus, the probability is $\boxed{\dfrac{25}{216}}$

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