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ray charles genius loves company - Decision Point

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Question: A glaciologist analyzes ice thickness data from 10 glaciers, 4 of which show rapid melting. If she selects 4 glaciers at random for detailed modeling, what is the probability that at least two of them are rapidly melting?

📌 Solution: We compute the probability of selecting at least 2 rapidly melting glaciers (out of 4 in total) from a group of 10, by summing favorable combinations.

📌 Total favorable = $90 + 24 + 1 = 115$

📌 Question: A philosopher of science considers 9 ethical frameworks used in climate research, 3 of which prioritize community impact. If she randomly selects 4 frameworks to analyze in a paper, what is the probability that all 3 community-focused frameworks are included?

📌 Solution: We compute the probability that all 3 community-focused frameworks are among the 4 selected.

📌 Solution: Since each altitude has one sensor, selecting 3 sensors with no two from the same altitude simply means choosing any 3 distinct sensors, which is guaranteed as all sensors are at different altitudes.

📌 All selections automatically have no two from the same altitude (all are unique by design), so favorable = 35

📌 Question: A glaciologist uses satellite data from 6 polar regions, 4 of which show significant glacier retreat. If she randomly selects 3 regions to present at a conference, what is the probability that at least one region without retreat is included?

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