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today number lottery - Sourci

📅 April 29, 2026 👤 scraface

Apr 29, 2026

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📌 Question: A historian notes that in a collection of 10 historical documents, 3 are written by Galileo, 4 by Newton, and 3 by Einstein. If the historian selects 4 documents at random, what is the probability that exactly two are written by Newton?

📌 Question: A biologist observes that a biologist from Europe arrives at a lab at a uniformly random time between 8:00 AM and 9:00 AM, while a biologist from Asia arrives at the same lab at a uniformly random time between 8:30 AM and 9:30 AM. What is the probability that the European biologist arrives before the Asian biologist?

📌 Total favorable = $0.5 + 0.375 = 0.875$. So probability is:

📌 But this contradicts intuition — the Asian biologist has a 1-hour shift from 8:30 to 9:30, while European has only 1 hour from 8:00 to 9:00. Actually, the overlap in time windows favors earlier arrival. But lets recompute with better geometry. The total sample space is a rectangle of width 1 (European time) and height 1 (Asian time), so area 1. The region $X < Y$:

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