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標題:

數學問題10A

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最佳解答:

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C=中文書E=英文書 given: 總共5C 4E，現隨意取4本 a) 取得 CCCC 5/9 x 4/8 x 3/7 x 2/6 = 0.397 (3 sig. fig.) b) 取得 CCCE 或 CCEC 或 CECC 或 ECCC (5/9 x 4/8 x 3/7 x 4/6) + (5/9 x 4/8 x 4/7 x 3/6) + (5/9 x 4/8 x 4/7 x 3/6) + (4/9 x 5/8 x 4/7 x 3/6) = (5/9 x 4/8 x 3/7 x 4/6) x4 = 0.317 (3 sig. fig) c) 取得 EEEE 或 EEEC 或 EECE 或 ECEE 或 CEEE (4/9 x 3/8 x 2/7 x 1/6) + (4/9 x 3/8 x 2/7 x 5/6) + (4/9 x 3/8 x 5/7 x 2/6) + (4/9 x 5/8 x 3/7 x 2/6) + (4/9 x 5/8 x 3/7 x 2/6) = (4/9 x 3/8 x 2/7 x 1/6) + (4/9 x 3/8 x 2/7 x 5/6) x4 = 0.007937 + 0.158730 = 0.167 (3 sig. fig)

其他解答:

a.) P(all chin.book) =(5/9)x(4/8)x(3/7)x(2/6) =5/126 b.) P(only 1 eng. books) =[(4/9)x(5/8)x(4/7)x(3/6)]+[(5/9)x(4/8)x(4/7)x(3/6)]+[(5/9)x(4/8)x(4/7)x(3/6)]+[(5/9)x(4/8)x(3/7)x(4/6)] =5/63+5/63+5/63+5/63 =20/63 c.) P(least 3 eng. books) =1-P(all chin.book)-P(only 1 eng. books) =1-5/126-20/63 =9/144E350C6F8B48ECA2