Suppose a jar contains 6 blue, 3 green, and 2 red marbles. What is the probability of randomly selecting three marbles such that at least two of them are the same color?
Suppose a jar contains 6 blue, 3 green, and 2 red marbles. What is the probability of randomly selecting three marbles such that at least two of them are the same color?
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:**Problem Statement:**
Suppose a jar contains 6 blue, 3 green, and 2 red marbles. What is the probability of randomly selecting three marbles such that at least two of them are the same color?
**Explanation:**
The problem involves calculating probabilities when selecting marbles from a jar. We're asked to find the probability that, out of three randomly selected marbles, at least two are of the same color.
**Steps to Solve:**
1. **Understand Total Possibilities:**
- The total marbles = 6 (blue) + 3 (green) + 2 (red) = 11 marbles.
- The total ways to choose 3 marbles out of 11 is calculated using combinations: \( C(11, 3) \).
2. **Calculate Probability:**
- Determine scenarios where at least two marbles are of the same color:
- Two or three marbles can be blue.
- Two or three marbles can be green.
- Two or three marbles can be red.
- These scenarios will include:
- Two blues and one of another color.
- Two greens and one of another color.
- Two reds and one of another color.
- Three blues, three greens, or three reds.
3. **Use Complementary Probability:**
- Alternatively, compute the probability of selecting three marbles all of different colors and subtract from 1.
- Calculate using combinations for the number of ways to choose one marble of each color.
4. **Result Interpretation:**
- The result will give the probability of picking at least two marbles with the same color from the jar.
This step-by-step approach helps in understanding how probability is applied in situations with multiple conditions.
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A jar contains 6 blue, 3 green and 2 red marbles.
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