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Home » The Must-Have Shelmet Everyone Is Talking About (Even You Need One!) - Treasure Valley Movers

The Must-Have Shelmet Everyone Is Talking About (Even You Need One!) - Treasure Valley Movers

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 Question: If three neurons each fire independently with a probability of $\frac{1}{4}$ per second, what is the probability that exactly one fires in a given second?

📌 Solution: Using the binomial distribution with $n = 3$, $p = \frac{1}{4}$, and $k = 1$:

📌 \binom{3}{1} \left(\frac{1}{4}\right)^1 \left(\frac{3}{4}\right)^2 = 3 \cdot \frac{1}{4} \cdot \frac{9}{16} = \frac{27}{64}.

📌 The probability is $\boxed{\dfrac{27}{64}}$.

📌 Question: How many ways can 4 identical water reserves be distributed into 3 distinct greenhouses, where each greenhouse can receive any number of reserves?

📌 Solution: This is a stars and bars problem. The formula for distributing $n$ identical items into $k$ distinct boxes is $\binom{n + k - 1}{k - 1}$. Here, $n = 4$, $k = 3$:

📌 \binom{4 + 3 - 1}{3 - 1} = \binom{6}{2} = 15.

📌 The number of ways is $\boxed{15}$.Question: Rationalize the denominator of $\frac{\sqrt{7} - 2}{\sqrt{7} + 3}$ and simplify the result.

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