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Answer the question in the screenshot below. Please write legibly and show your work. Thank you! 1. Amongst students one of the questions asked was

Answer the question in the screenshot below. Please write legibly and show your work. Thank you!

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1. Amongst students one of the questions asked was whether their primary goal was to get good grades, be popular or be good at sports. The following 2-way table gives the counts. Grades Popular Sports Boys 117 50 60 Girls 130 91 30 Find the following probabilities. Show some work for each. a. P(girl): b. P(girl and popular): c. P(girl or popular): d. P(sports|girl): e. P(boy|grades): f. Are the events "Girl" and "Sports" independent? Verify your conclusion mathematically. Explain your results

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