Problems 3 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.) Increased (X) Decreased (Y) Unchanged (Z) Totals Financials (F) 3 4 1 8 Manufacturing (M) 8 3 3 14 Information Technology (T) 6 0 7 Health Care (H) 4 1 1 6 Utilities (U) 3 1 1 5 Totals 24 10 6 40 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. (c) That it was a manufacturing industry and its stock market performance increased. (d) That it was a manufacturing industry or its stock market performance increased.