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Home » A point on the line: \(\mathbfr_0 = eginpmatrix 1 \ -2 \endpmatrix\) - AMAZONAWS

A point on the line: \(\mathbfr_0 = eginpmatrix 1 \ -2 \endpmatrix\) - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 There are 12 sides on the die, and the numbers divisible by 4 are 4, 8, and 12, so 3 out of 12 faces are favorable.

📌 Thus, the probability of rolling a number divisible by 4 is $ \frac{3}{12} = \frac{1}{4} $, and the probability of **not** rolling a multiple of 4 is $ 1 - \frac{1}{4} = \frac{3}{4} $.

📌 We want exactly one of the three rolls to be divisible by 4. This is a binomial probability:

📌 P(\text{exactly one success}) = \binom{3}{1} \left(\frac{1}{4}\right)^1 \left(\frac{3}{4}\right)^2 = 3 \cdot \frac{1}{4} \cdot \frac{9}{16} = \frac{27}{64}

📌 So the probability is $ \boxed{\frac{27}{64}} $.

📌 Question: A biotechnology educator uses 6 different colored vials: 2 red, 2 blue, and 2 green. If she randomly selects 3 vials without replacement, what is the probability that all 3 are of different colors?

📌 Total number of ways to choose 3 vials from 6:

📌 To get one vial of each color, we choose one red, one blue, and one green. There are 2 choices for each color:

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