A research group conducted a national survey of 450 small-business owners to determine the challenges for growth for their businesses. A total of 177 said that the biggest challenge was the economy, while 126 said the biggest challenge was finding qualified workers. Sixty-seven respondents selected both the economy and finding qualified workers as challenges for growth. Let E be the event that a business owner selected the economy as the biggest challenge and let W be the event that a business owner selected finding qualified workers as the biggest challenge. A small business owner from the surveyed group is selected.
 

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a. W Wc Create a joint probability table for the events E, ES, W, and W. Total Total E E b. What is the probability that the owner chose neither the economy nor finding qualified workers as a challenge for growth? c. Given that an owner chose the economy as a challenge for growth (E), what is the probability that they also chose finding qualified workers (W)? d. Are events E and W independent? Justify your answer with calculated probabilities. a. W Wc Create a joint probability table for the events E, ES, W, and W. Total Total E E b. What is the probability that the owner chose neither the economy nor finding qualified workers as a challenge for growth? c. Given that an owner chose the economy as a challenge for growth (E), what is the probability that they also chose finding qualified workers (W)? d. Are events E and W independent? Justify your answer with calculated probabilities. a. W Wc Create a joint probability table for the events E, ES, W, and W. Total Total E E b. What is the probability that the owner chose neither the economy nor finding qualified workers as a challenge for growth? c. Given that an owner chose the economy as a challenge for growth (E), what is the probability that they also chose finding qualified workers (W)? d. Are events E and W independent? Justify your answer with calculated probabilities. a. W Wc Create a joint probability table for the events E, ES, W, and W. Total Total E E b. What is the probability that the owner chose neither the economy nor finding qualified workers as a challenge for growth? c. Given that an owner chose the economy as a challenge for growth (E), what is the probability that they also chose finding qualified workers (W)? d. Are events E and W independent? Justify your answer with calculated probabilities. a. W Wc Create a joint probability table for the events E, ES, W, and W. Total Total E E b. What is the probability that the owner chose neither the economy nor finding qualified workers as a challenge for growth? c. Given that an owner chose the economy as a challenge for growth (E), what is the probability that they also chose finding qualified workers (W)? d. Are events E and W independent? Justify your answer with calculated probabilities. a. W Wc Create a joint probability table for the events E, ES, W, and W. Total Total E E b. What is the probability that the owner chose neither the economy nor finding qualified workers as a challenge for growth? c. Given that an owner chose the economy as a challenge for growth (E), what is the probability that they also chose finding qualified workers (W)? d. Are events E and W independent? Justify your answer with calculated probabilities.

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a E Ec Total W 67 59 126 Wc 110 214 324 Total 177 273 450 b ... View the full answer