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2023 afc championship game - Sourci

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 \times 243 = 4860

📌 Thus, the virologist can observe $\boxed{4860}$ valid genome configurations.

📌 Question: A science fair judge evaluates 7 student projects, each judged on creativity (C), scientific rigor (R), and presentation (P), with each project receiving a score in each category: high (H) or low (L). The judge considers a project Exceptionally Strong if it receives high scores in at least 5 of the 3 categories. Assuming each score is independently high with probability $ \frac{1}{2} $, what is the probability that exactly 3 out of the 7 projects are Exceptionally Strong?

📌 Solution: First, compute the probability that a single project is Exceptionally Strong, i.e., gets H in at least 5 of the 3 categories. But there are only 3 categories, so getting high in at least 5 is impossible.

📌 Wait — this is a contradiction. A project cannot get high scores in more than 3 categories. The condition at least 5 high scores is impossible.

📌 But the problem says: high in at least 5 of the 3 categories — which is logically impossible.

📌 Thus, the probability is 0.

📌 Therefore, the number of Exceptionally Strong projects among 7 is a binomial random variable with $n = 7$, $p = 0$, because $p(\text{≥5 H}) = 0$ for 3 categories.

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