The California Department of Labor surveyed the relationship between gender and the occupation. The table below shows the number of female and male workers in each occupational category. Occupation Females Males Business 1400 1300 IT 500 700 Legal service 1800 1000 Manufacturing 200 900 Hospitality 100 900 Healthcare 900 100 Total 4900 4900 a) Given that a worker is a male, what is the probability that he works in hospitality? b) Is occupation independent of gender? (Justify your answer with a probability calculation like question 2e, you can use your answer from 3a to answer this question).Question 4 (Bayes Theorem) The U.S.'s three largest import regions are North America (consisting of Mexico and Canada), and Northeast Asia (China, Japan, and South Korea). Imports from North America consist of approximately 10% (.10) of all imports to the U.S., imports from Northeast Asia make up approximately 40% (.40) of all imports, and 50% (.50) of imports to the US come from other regions or countries. The U.S. also imports a significant number of electronic devices. 12% (.12) of imports from North America are electronic devices, 50% (.50) of the goods imported from Northeast Asia are electronic devices, and 5% (.05) of goods imported from elsewhere are electronic devices. If you purchase an imported electronic device, what is the probability that it is imported from Northeast Asia? {Show all work, including picture ondformulos)