Pregunta
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\( \begin{array}{r}\text { A bag has } 20 \text { cubes in it. } 6 \text { of the cubes are green. } \\ \text { You take one cube out of the bag at random. }\end{array} \) \( \begin{array}{lllll}\frac{6}{14} & 30 \% & 0.6 & \frac{3}{10} \\ \text { Which four values below show the probability that you take out a cube that is green? }\end{array} \) \( \begin{array}{lllll}6 \% & \frac{3}{5} & \frac{6}{20} & 0.03 \\ 0.3 & \frac{6}{10} & 60 \% & \frac{6}{26}\end{array} \) Q zoom

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Jan 06,2025

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The correct probabilities are 30%, 3⁄10, 6⁄20, and 0.3.

Solución

To determine the probability of drawing a green cube from the bag, let's break down the problem: - **Total cubes in the bag:** 20 - **Green cubes:** 6 **Probability Formula:** \[ \text{Probability} = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} = \frac{6}{20} \] Simplifying the fraction: \[ \frac{6}{20} = \frac{3}{10} = 0.3 = 30\% \] So, the probability of drawing a green cube can be represented in four different ways: 1. \(\frac{6}{20}\) 2. \(\frac{3}{10}\) 3. \(0.3\) 4. \(30\%\) **From the provided options:** - **First Row:** - \(6/14\) ➔ **Incorrect** - **30\%** ➔ **Correct** - \(0.6\) ➔ **Incorrect** - **\(\frac{3}{10}\)** ➔ **Correct** - **Second Row:** - \(6\%\) ➔ **Incorrect** - \(3/5\) ➔ **Incorrect** - **\(6/20\)** ➔ **Correct** - \(0.03\) ➔ **Incorrect** - **\(0.3\)** ➔ **Correct** - \(6/10\) ➔ **Incorrect** - \(60\%\) ➔ **Incorrect** - \(6/26\) ➔ **Incorrect** **Therefore, the four correct values are:** - \(30\%\) - \(\frac{3}{10}\) - \(6/20\) - \(0.3\) **Answer:** The four correct probabilities are 30 %, 3⁄10, 6⁄20, and 0.3.

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Bonus Knowledge

To find the probability of drawing a green cube from the bag, you take the number of green cubes (6) and divide it by the total number of cubes (20). This gives you \( \frac{6}{20} \), which simplifies to \( \frac{3}{10} \) or 30%. So, these can be expressed in different forms: \( \frac{3}{10} \), \( 0.3 \), or 30%. Here’s a fun fact: the concept of probability dates back centuries, with roots in games of chance! In the 16th century, mathematicians began to formalize the rules, making it easier to understand chance events like this one. For a real-world application, think about how probability helps in making decisions. If you're considering a green cube for a game or activity and know the probability, you can better predict outcomes. For instance, if a friend asks you to pick a cube and you want the chance of it being green, knowing that there's a 30% chance can help inform your strategizing!

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