數學問題10A

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)

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
=9/14