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Home » You Won’t Believe How 2 Meters Equals Exactly How Many Inches! - Dachbleche24

You Won’t Believe How 2 Meters Equals Exactly How Many Inches! - Dachbleche24

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 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.

📌 Hence, the probability that exactly 3 projects are Exceptionally Strong is:

📌 \binom{7}{3} \cdot 0^3 \cdot (1 - 0)^4 = 0

📌 Thus, the probability is $\boxed{0}$.

📌 Question: A robotics engineer is testing a robot that moves on a grid, making exactly 8 steps from the origin $(0,0)$ to some point $(x,y)$, with each step either increasing $x$ by 1 or $y$ by 1. The robot must end at a point where $x + y = 8$, $x \geq 3$, and output $x$ if $x \geq 4$, or $y$ if $x < 4$. What is the expected value of the output?

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