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Home » Radius \( r = \frac142 = 7 \) cm. - Dachbleche24

Radius \( r = \frac142 = 7 \) cm. - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 Next, we compute the number of favorable outcomes: selecting exactly 2 red, 2 green, and 2 blue grains. Since there are 5 red grains, 3 green, and 2 blue, the number of favorable combinations is:

📌 \binom{5}{2} \times \binom{3}{2} \times \binom{2}{2} = 10 \times 3 \times 1 = 30

📌 \frac{30}{210} = \frac{1}{7}

📌 \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:

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