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The probability of drawing a red marble from a sack of marbles is . Which set of marbles could the sack contain 02 red marbles and 5 green marbles 04 red marbles and 6 green marbles 06 red marbles and 15 green marbles 02 red marbles, I blue marble, and 4 white marbles

The probability of drawing a red marble from a sack of marbles is . Which set of marbles could the sack contain 02 red marbles and 5 green marbles 04 red marbles and 6 green marbles 06 red marbles and 15 green marbles 02 red marbles, I blue marble, and 4 white marbles

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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**Question:** The probability of drawing a red marble from a sack of marbles is \( \frac{1}{3} \). Which set of marbles could the sack contain? - 2 red marbles and 5 green marbles - 4 red marbles and 6 green marbles - 6 red marbles and 15 green marbles - 2 red marbles, 1 blue marble, and 4 white marbles **Explanation:** To solve this problem, determine which set of marbles results in a probability of \( \frac{1}{3} \) for drawing a red marble. **Steps:** 1. Calculate the total number of marbles for each option. 2. Calculate the probability of drawing a red marble in each case. 3. Match the calculated probability with \( \frac{1}{3} \). - **First option:** 2 red marbles + 5 green marbles = 7 marbles total - Probability = \( \frac{2}{7} \) - **Second option:** 4 red marbles + 6 green marbles = 10 marbles total - Probability = \( \frac{4}{10} = \frac{2}{5} \) - **Third option:** 6 red marbles + 15 green marbles = 21 marbles total - Probability = \( \frac{6}{21} = \frac{2}{7} \) - **Fourth option:** 2 red marbles + 1 blue marble + 4 white marbles = 7 marbles total - Probability = \( \frac{2}{7} \) The correct probability of \( \frac{1}{3} \) does not match any options through simple calculation, indicating there might be an error in the problem setup or options provided.
Transcribed Image Text:**Question:** The probability of drawing a red marble from a sack of marbles is \( \frac{1}{3} \). Which set of marbles could the sack contain? - 2 red marbles and 5 green marbles - 4 red marbles and 6 green marbles - 6 red marbles and 15 green marbles - 2 red marbles, 1 blue marble, and 4 white marbles **Explanation:** To solve this problem, determine which set of marbles results in a probability of \( \frac{1}{3} \) for drawing a red marble. **Steps:** 1. Calculate the total number of marbles for each option. 2. Calculate the probability of drawing a red marble in each case. 3. Match the calculated probability with \( \frac{1}{3} \). - **First option:** 2 red marbles + 5 green marbles = 7 marbles total - Probability = \( \frac{2}{7} \) - **Second option:** 4 red marbles + 6 green marbles = 10 marbles total - Probability = \( \frac{4}{10} = \frac{2}{5} \) - **Third option:** 6 red marbles + 15 green marbles = 21 marbles total - Probability = \( \frac{6}{21} = \frac{2}{7} \) - **Fourth option:** 2 red marbles + 1 blue marble + 4 white marbles = 7 marbles total - Probability = \( \frac{2}{7} \) The correct probability of \( \frac{1}{3} \) does not match any options through simple calculation, indicating there might be an error in the problem setup or options provided.
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