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Problems 3 and 4 are based on the following table which shows the stock market...

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Problems 3 and 4 are based on the following table which shows the stock market performance of 40 industries from five sectors of the U S economy as of noon on September 11 2015 Take S to be the set of all 40 industries represented in the table Hint Similar to Section 6 2 Exercises 47 and 51 in the book Decreased Y Financials F Manufacturing M Increased X OLUWBUD Unchanged Z Totals 4 1 8 Information Technology T Health Care H 4 Utilities U 3 Totals 24 3 10 6 1 1 3 6 1 1 3 40 8 0 6 5 14 7 3 Calculate the following probabilities for an industry selected at random from all those represented in the table a That its stock market performance increased given that it was a manufacturing industry b That it was a manufacturing industry given that its stock market performance increased industry and its stock market performance increased

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