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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 \boxed{\frac{1}{7}}

📌 Question: A wildlife researcher is analyzing the genetic diversity of a population of 10 endangered gorillas. If 4 of them are tagged with GPS collars, and the researcher selects 3 gorillas at random for detailed monitoring, what is the probability that at least one of the selected gorillas has a GPS collar?

📌 We compute the probability of the complement event: selecting 3 gorillas with **none** having GPS collars. There are 6 gorillas without GPS collars, so the number of ways to choose 3 without GPS collars is:

📌 The total number of ways to choose any 3 gorillas from the 10 is:

📌 So, the probability that none of the selected gorillas have GPS collars is:

📌 \frac{20}{120} = \frac{1}{6}

📌 Therefore, the probability that **at least one** has a GPS collar is:

📌 - \frac{1}{6} = \frac{5}{6}

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