A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
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Scott wakes up late on average 3 days in every 5. If Scott wakes up late, the probability he’s late for school is 9/10. If Scott does not wake up late, the probability he’s late for school is 3/10. Complete the tree diagram to calculate what percent of the days Scott is late to school?
Transcribed Image Text:This image is a probability tree diagram used to determine the likelihood of arriving at school late or on time based on whether a person wakes up late or on time.
### Explanation of the Diagram:
1. **Initial Split**:
- The first decision point is whether the individual wakes late or on time.
- **Wakes late** has a probability of \( \frac{3}{5} \).
- **Wakes on time** has a probability of \( \frac{2}{5} \).
2. **Second Level Outcomes**:
- Given that a person wakes late:
- The probability of being **school late** is \( \frac{9}{10} \).
- The probability of being **school on time** is \( \frac{1}{10} \).
- Given that a person wakes on time:
- The probability of being **school late** is \( \frac{3}{10} \).
- The probability of being **school on time** is \( \frac{7}{10} \).
### Summary:
The tree structure helps visualize compound probabilities by breaking them into sequential stages. The probability of each outcome is computed by multiplying the probabilities along the branches. This tool is useful in educational settings for teaching probability concepts and decision-making processes.
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