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Home » Using \( f\left(\frac\pi2b\right) = 4 \): - Appfinity Technologies

Using \( f\left(\frac\pi2b\right) = 4 \): - Appfinity Technologies

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 A linguist compares two dialects and finds that 78% of core vocabulary matches. If the corpus contains 1,200 cognates, how many do not match?

📌 Matched: 78% of 1,200 = 0.78 × 1,200 = 936

📌 Not matched: 1,200 − 936 = 264

📌 #### 264Question: An epidemiologist models the spread of a virus where each infected person has a $\frac{1}{3}$ chance of transmitting it to a contact. What is the probability that exactly 2 out of 4 contacts become infected?

📌 Solution: The probability follows a binomial distribution with parameters $n = 4$ (trials) and $p = \frac{1}{3}$ (success probability). The formula for exactly $k$ successes is $\binom{n}{k} p^k (1-p)^{n-k}$. For $k = 2$:

📌 \binom{4}{2} \left(\frac{1}{3}\right)^2 \left(\frac{2}{3}\right)^2 = 6 \cdot \frac{1}{9} \cdot \frac{4}{9} = \frac{24}{81} = \frac{8}{27}.

📌 The probability is $\boxed{\dfrac{8}{27}}$.

📌 Question: A neural interface system processes 5 distinct signals using 3 unique channels. How many ways can the signals be assigned to channels if each channel can process any number of signals?

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