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8. It is reported that 77% of workers aged 16 and over drive to work alone. Choose 4 workers at random. Find the probability that: a. All drive to work alone b. One of them drives to work alone C. More than one of them drives to work alone

8. It is reported that 77% of workers aged 16 and over drive to work alone. Choose 4 workers at random. Find the probability that: a. All drive to work alone b. One of them drives to work alone C. More than one of them drives to work alone

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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Certainly! Here's the transcription suitable for an educational website: --- **Probability Problem:** It is reported that 77% of workers aged 16 and over drive to work alone. If you choose 4 workers at random, calculate the probability for each of the following scenarios: a. All drive to work alone. b. One of them drives to work alone. c. More than one of them drives to work alone. --- **Solution Approach:** 1. **Probability Fundamentals:** - Probability of a worker driving alone = 77% = 0.77 - Probability of a worker not driving alone = 1 - 0.77 = 0.23 2. **Calculating the Probabilities:** - Use binomial probability formulas or distributions to calculate each scenario. **Exploration:** - For scenario (a), calculate \((0.77)^4\). - For scenario (b), choose one driver (\(4 \times (0.77)^1\) and the rest as \((0.23)^3\)). - For scenario (c), find the complement of one or zero driving alone. This framework will help guide exploring probability through practical examples.
Transcribed Image Text:Certainly! Here's the transcription suitable for an educational website: --- **Probability Problem:** It is reported that 77% of workers aged 16 and over drive to work alone. If you choose 4 workers at random, calculate the probability for each of the following scenarios: a. All drive to work alone. b. One of them drives to work alone. c. More than one of them drives to work alone. --- **Solution Approach:** 1. **Probability Fundamentals:** - Probability of a worker driving alone = 77% = 0.77 - Probability of a worker not driving alone = 1 - 0.77 = 0.23 2. **Calculating the Probabilities:** - Use binomial probability formulas or distributions to calculate each scenario. **Exploration:** - For scenario (a), calculate \((0.77)^4\). - For scenario (b), choose one driver (\(4 \times (0.77)^1\) and the rest as \((0.23)^3\)). - For scenario (c), find the complement of one or zero driving alone. This framework will help guide exploring probability through practical examples.
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