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You have a jar of marbles in front of you with the following colors: 12 red, 17 blue, 8 yellow, and 13 white. Suppose you had a larger jar of 250 fnarbles with the same ratio of colors. What is the probability of randomly selecting either a red or white marble from the larger jar

Ask by Cervantes Boone. in the United States
Feb 13,2025

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Answer

The probability of randomly selecting either a red or white marble from the larger jar is 1/2 or 50%.

Solution

Step 1: Determine the total number of marbles in the original jar.   Red = 12, Blue = 17, Yellow = 8, White = 13   Total = 12 + 17 + 8 + 13 = 50 Step 2: Calculate the number of red or white marbles.   Red + White = 12 + 13 = 25 Step 3: Compute the probability for a red or white marble.   Probability = (Red + White) / Total = 25 / 50 = 1/2 Since the larger jar of 250 fnarbles maintains the same ratios of colors, the probability of drawing a red or white marble remains 1/2 (or 50%).

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To find the probability of selecting a red or white marble, first, determine the total number of marbles in the smaller jar, which is 12 (red) + 17 (blue) + 8 (yellow) + 13 (white) = 50 marbles. The ratio of red to white marbles is 12 + 13 = 25. Now, considering the larger jar of 250 marbles, calculate the number of each color: (12/50) * 250 for red gives you 60 red marbles, and (13/50) * 250 for white gives you 65 white marbles. Thus, the total red and white marbles is 60 + 65 = 125. The probability of selecting a red or white marble is 125/250, which simplifies to 1/2 or 50%. By exploring the concept of probability, you not only understand how to calculate chances but also appreciate its applications in everyday decisions! Whether it's picking a marble, choosing a movie, or even guessing the weather—probability helps us weigh options and make educated choices. If you’re curious about enhancing your probability skills, consider diving into topics like combinatorics or statistics. Resources like Khan Academy or “The Drunkard's Walk” by Leonard Mlodinow offer engaging insights and fun ways to grasp complex ideas. Learning through real-world examples can provide a solid foundation and make the subject matter feel less daunting!

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