A First Course in Probability (10th Edition)
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ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Transcribed Image Text:**Predicting the Number of Red Beads in Gerald's Bag**
**Problem Statement:**
Gerald buys a bag of 7,500 assorted beads online. A random sample of 150 beads contains 17 red beads. Predict the number of red beads in the bag of assorted beads that Gerald bought.
**Solution:**
To predict the number of red beads in the entire bag, we can use proportions. Here's a step-by-step method:
1. Determine the proportion of red beads in the sample.
- Number of red beads in the sample: 17
- Total number of beads in the sample: 150
Proportion of red beads in the sample = \(\frac{17}{150}\)
2. Use this proportion to predict the number of red beads in the entire bag.
- Total number of beads in the bag: 7,500
Predicted number of red beads = Proportion of red beads in the sample \(\times\) Total number of beads in the bag
Predicted number of red beads = \(\frac{17}{150} \times 7500\)
3. Calculate the result:
- \(\frac{17}{150}\) ≈ 0.1133
- 0.1133 \(\times\) 7500 ≈ 849.75
Therefore, we can predict that there are approximately 850 red beads in the bag of 7,500 assorted beads that Gerald bought.
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