ᱨᱩᱞᱮᱴ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ
ᱨᱩᱞᱮᱴ ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ ᱠᱷᱟᱱᱟ ᱞᱮᱠᱷᱟ ᱮᱛᱚᱢ 37 ᱛᱮ ᱦᱟᱹᱴᱤᱧ ᱠᱟᱱᱟ᱾
p = ᱥᱟᱵ ᱟᱠᱟᱱ ᱮᱞ / 37᱾ ᱢᱤᱫ ᱮᱞ: 2.70%᱾ ᱜᱮᱞ ᱤᱨᱟᱹᱞ: 48.65%᱾ ᱢᱤᱫ ᱴᱷᱤᱠ ᱞᱟᱹᱲᱤ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ ᱢᱤᱫᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱠᱚ ᱜᱩᱱ ᱠᱟᱛᱮ ᱧᱟᱢᱚᱜ-ᱟ᱾
ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ
37 ᱜᱚᱴᱟᱝ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱡᱚᱛᱚ ᱜᱮ ᱥᱚᱢᱟᱱ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱢᱮᱱᱟᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱨᱩᱞᱮᱴ ᱨᱮ ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ ᱞᱮᱠᱷᱟ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱜᱮ᱾ ᱯᱩᱱ ᱮᱞ ᱨᱮ ᱵᱟᱡᱤ ᱫᱚ 37 ᱫᱷᱟᱣ ᱠᱷᱚᱱ 4 ᱫᱷᱟᱣ ᱡᱤᱛᱚᱜ-ᱟ, ᱠᱚᱢ ᱵᱮᱥᱤ 10.8%᱾ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱱᱚᱣᱟ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱡᱟᱦᱟᱸᱱᱟᱜ ᱵᱟᱹᱱᱩᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱜᱚᱴᱟ ᱠᱷᱮᱞ ᱫᱚ ᱢᱤᱫ ᱦᱩᱰᱤᱧ ᱠᱟᱜᱚᱡ ᱨᱮ ᱦᱤᱥᱟᱹᱵ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾
ᱟᱭᱢᱟ ᱜᱷᱩᱨᱟᱹᱣ
ᱜᱷᱩᱨᱟᱹᱣ ᱠᱚ ᱟᱡᱟᱫ ᱠᱟᱱᱟ, ᱚᱱᱟᱛᱮ ᱢᱤᱫ ᱞᱟᱹᱲᱤ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱠᱚ ᱜᱩᱱᱚᱜ-ᱟ᱾ ᱞᱟᱜᱟᱛᱟᱨ ᱵᱟᱨ ᱫᱷᱟᱣ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →: (18/37)² = 23.7%᱾ ᱟᱨᱟᱜ ᱛᱟᱭᱚᱢ ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →: (18/37)(1/37) = 1.3%᱾ ᱞᱟᱜᱟᱛᱟᱨ ᱵᱟᱨ ᱫᱷᱟᱣ ᱜᱮᱞ ᱮᱭᱟᱭ: (1/37)² = 0.073%, ᱠᱚᱢ ᱵᱮᱥᱤ 1,369 ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱢᱤᱫ ᱴᱷᱤᱠ ᱞᱟᱹᱲᱤ ᱞᱟᱹᱜᱤᱫ ᱛᱟᱹᱞᱤ ᱫᱚ ᱞᱟᱹᱠᱛᱤ ᱜᱮᱭᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱞᱮᱠᱷᱟ ᱞᱟᱹᱜᱤᱫ ᱫᱚ ᱵᱟᱝ: “ᱟᱨᱟᱜ ᱛᱟᱭᱚᱢ ᱦᱮᱸᱫᱮᱵᱟᱡᱤᱦᱮᱸᱫᱮ18 ᱦᱮᱸᱫᱮ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱱᱣᱟᱨ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ →” ᱫᱚ 25.0% ᱠᱟᱱᱟ, ᱢᱮᱱᱠᱷᱟᱱ “ᱵᱟᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱟᱨᱟᱜ ᱟᱨ ᱢᱤᱫ ᱦᱮᱸᱫᱮ, ᱡᱟᱦᱟᱸ ᱛᱟᱹᱞᱤ ᱛᱮ ᱦᱚᱸ” ᱫᱚ 50.0% ᱠᱟᱱᱟ᱾
ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱢᱤᱫ ᱫᱷᱟᱣ
ᱵᱟᱠᱤ ᱦᱟᱹᱴᱤᱧ ᱵᱮᱵᱷᱟᱨ ᱯᱮ᱾ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱚᱸ ᱵᱟᱝ ᱩᱫᱩᱜᱚᱜ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ (36/37)³⁷ = 36.3% ᱠᱟᱱᱟ, ᱚᱱᱟᱛᱮ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱢᱤᱫ ᱫᱷᱟᱣ ᱩᱫᱩᱜᱚᱜ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ 63.7% ᱠᱟᱱᱟ; 37 ᱠᱷᱚᱱ 1 ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱥᱟᱶ 37 ᱫᱷᱟᱣ ᱠᱷᱮᱞ ᱠᱟᱛᱮ ᱟᱭᱢᱟ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱡᱟᱦᱟᱸ “ᱥᱟᱹᱨᱤ ᱜᱮ” ᱟᱥᱟ ᱠᱚ ᱠᱟᱹᱢᱤᱭᱟ, ᱚᱱᱟ ᱫᱚ ᱵᱟᱝ᱾ ᱚᱱᱟ ᱦᱤᱥᱟᱹᱵ ᱜᱮ ᱢᱮᱱᱮᱫᱟ ᱡᱮ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱮᱞ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱚᱸ ᱵᱟᱝ ᱩᱫᱩᱜᱚᱜ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ 3 ᱠᱷᱚᱱ 1 ᱠᱟᱱᱟ, ᱚᱱᱟᱛᱮ ᱨᱮᱡᱟᱞᱴ ᱵᱳᱨᱰ ᱨᱮ ᱥᱟᱵᱟᱫᱚ ᱛᱤᱱᱟᱹᱜ “ᱴᱷᱟᱸᱰᱟ” ᱮᱞ ᱧᱮᱞᱚᱜ-ᱟ᱾
ᱟᱸᱫᱟᱡᱽ ᱛᱟᱹᱝᱜᱤ ᱚᱠᱛᱚ
ᱟᱣᱥᱚᱛ ᱛᱮ ᱢᱤᱫ ᱥᱴᱨᱮᱴ ᱚᱯ ᱮᱞ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱩᱫᱩᱜᱚᱜ-ᱟ, ᱢᱮᱱᱠᱷᱟᱱ ᱛᱟᱹᱝᱜᱤ ᱚᱠᱛᱚ ᱫᱚ ᱟᱹᱰᱤ ᱵᱚᱫᱚᱞᱚᱜ-ᱟ: ᱢᱤᱰᱤᱭᱟᱱ ᱛᱟᱹᱝᱜᱤ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ 25 ᱜᱷᱩᱨᱟᱹᱣ (ᱟᱫᱷᱟ ᱫᱷᱟᱣ ᱚᱱᱟ ᱠᱷᱚᱱ ᱞᱟᱦᱟ ᱩᱫᱩᱜᱚᱜ-ᱟ) ᱟᱨ ᱵᱤᱥ ᱛᱟᱹᱝᱜᱤ ᱠᱷᱚᱱ ᱢᱤᱫ ᱫᱚ 110 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱦᱩᱭᱩᱜ-ᱟ᱾ ᱡᱤᱭᱚᱢᱮᱴᱨᱤᱠ ᱯᱨᱚᱥᱮᱥ ᱨᱮᱭᱟᱜ ᱛᱟᱹᱝᱜᱤ ᱚᱠᱛᱚ ᱨᱮ ᱡᱮᱞᱮᱧ ᱪᱩᱞᱟᱹ ᱢᱮᱱᱟᱜ-ᱟ, ᱟᱨ ᱡᱟᱦᱟᱸ ᱠᱷᱮᱞᱚᱸᱰ 60 ᱜᱷᱩᱨᱟᱹᱣ ᱛᱟᱭᱚᱢ ᱢᱤᱫ ᱮᱞ ᱫᱚ ᱦᱮᱡ ᱦᱚᱨ ᱠᱟᱱᱟ ᱢᱮᱱᱛᱮ “ᱵᱟᱰᱟᱭ” ᱟᱭ, ᱩᱱᱤ ᱫᱚ ᱢᱚᱬᱮ ᱫᱷᱟᱣ ᱠᱷᱚᱱ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱩᱭᱩᱜ ᱠᱟᱛᱷᱟ ᱜᱮ ᱞᱟᱹᱭ ᱮᱫᱟᱭ᱾
ᱥᱟᱫᱷᱟᱨᱚᱬ ᱵᱷᱩᱞ
ᱵᱟᱨᱭᱟ ᱜᱮ ᱥᱟᱶᱛᱮ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱡᱚᱲᱟᱣ (ᱟᱨᱟᱜ ᱟᱨᱵᱟᱝ ᱵᱤᱡᱳᱲ ᱫᱚ 36/37 ᱵᱟᱝ; 26/37 ᱠᱟᱱᱟ, ᱪᱮᱫᱟᱜ ᱥᱮ ᱜᱮᱞ ᱮᱞ ᱫᱚ ᱵᱟᱨᱭᱟ ᱜᱮ ᱠᱟᱱᱟ)᱾ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱞᱟᱹᱜᱤᱫ ᱜᱩᱱ (ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱨᱟᱜ ᱟᱨ ᱵᱤᱡᱳᱲ ᱫᱚ 10/37 ᱠᱟᱱᱟ, 18/37 × 18/37 ᱵᱟᱝ)᱾ ᱢᱟᱨᱮ ᱜᱷᱩᱨᱟᱹᱣ ᱠᱚ ᱱᱤᱛ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱞᱟᱹᱲᱤ ᱨᱮᱭᱟᱜ ᱦᱟᱹᱴᱤᱧ ᱞᱮᱠᱟ ᱵᱩᱡᱷᱟᱹᱣ: ᱜᱮᱞ ᱟᱨᱟᱜ ᱛᱟᱭᱚᱢ, ᱜᱮᱞᱢᱤᱫ ᱟᱨᱟᱜ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ 18/37 ᱠᱟᱱᱟ, (18/37)¹¹ ᱵᱟᱝ᱾
ᱨᱩᱞᱮᱴ ᱨᱮ ᱚᱰᱥ ᱫᱚ ᱪᱮᱫ ᱠᱟᱱᱟ, ᱟᱨ ᱚᱠᱟ ᱞᱮᱠᱟ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱠᱷᱚᱱ ᱵᱷᱮᱜᱟᱨ?
ᱠᱮᱥᱤᱱᱳ ᱫᱚ ᱵᱷᱩᱜᱛᱟᱱᱴᱟᱠᱟᱵᱷᱩᱜᱛᱟᱱᱡᱤᱛ ᱵᱟᱡᱤ ᱪᱮᱫ ᱨᱩᱣᱟᱹᱲᱟ, ᱨᱩᱣᱟᱹᱲ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱪᱮᱛᱟᱱ “X ᱨᱮ 1” ᱞᱮᱠᱟ ᱨᱚᱲᱚᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱚᱰᱥ ᱞᱮᱠᱟ ᱛᱮ ᱠᱚ ᱞᱟᱹᱭᱟ᱾ ᱢᱤᱫ ᱮᱞ ᱫᱚ 1/37 ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱮ ᱡᱤᱛᱚᱜ-ᱟ, ᱚᱱᱟᱛᱮ ᱢᱤᱫ ᱮᱞ ᱨᱮ ᱨᱩᱞᱮᱴ ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱚᱰᱥ ᱫᱚ 36 ᱨᱮ 1 ᱵᱤᱨᱩᱫᱷ ᱠᱟᱱᱟ᱾ ᱚᱱᱟᱛᱮ 35 ᱨᱮ 1 ᱵᱷᱩᱜᱛᱟᱱ ᱫᱚ ᱢᱤᱫ ᱭᱩᱱᱤᱴᱴᱟᱠᱟᱭᱩᱱᱤᱴᱢᱤᱫ ᱥᱤᱥᱴᱮᱢ ᱟᱨᱵᱟᱝ ᱠᱷᱮᱞᱚᱸᱰ ᱵᱮᱵᱷᱟᱨ ᱵᱮᱥ ᱵᱟᱡᱤ ᱴᱟᱠᱟ᱾ ᱯᱨᱚᱜᱽᱨᱮᱥᱚᱱ ᱠᱚ ᱭᱩᱱᱤᱴ ᱛᱮ ᱵᱩᱡᱷᱟᱹᱣᱚᱜ-ᱟ ᱡᱮᱢᱚᱱ ᱡᱟᱦᱟᱸᱱ ᱴᱮᱵᱩᱞ ᱨᱮ ᱞᱟᱹᱜᱩ ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱚᱢ ᱠᱟᱱᱟ, ᱟᱨ ᱱᱚᱣᱟ ᱜᱮ ᱫᱚ ᱟᱥᱚᱞ ᱨᱩᱯ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤᱜᱚᱱᱤᱛᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤᱡᱚᱛᱚ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱠᱷᱚᱱ ᱠᱮᱥᱤᱱᱳ ᱟᱣᱥᱚᱛ ᱛᱮ ᱫᱚᱦᱚᱭ ᱦᱟᱹᱴᱤᱧ: ᱭᱩᱨᱚᱯᱤᱭᱟᱱ ᱨᱩᱞᱮᱴ ᱨᱮ 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱠᱟᱱᱟ᱾ ᱵᱚᱫᱚᱞ: ᱵᱤᱨᱩᱫᱷ ᱚᱰᱥ = (1 − p)/p; ᱥᱚᱢᱵᱷᱟᱵᱱᱟ = 1/(ᱚᱰᱥ + 1)᱾
ᱯᱷᱚᱨᱢᱩᱞᱟ
ᱠᱩᱠᱞᱤ ᱠᱚ
(1/37)² = 1/1369 ≈ 0.073%.
36/37 = 97.3%᱾ ᱵᱟᱠᱤ ᱫᱚ ᱡᱤᱨᱚ ᱠᱟᱱᱟ᱾
ᱡᱚᱛᱚ 37 ᱮᱞ ᱜᱮ 1/37 ᱠᱟᱱᱟ᱾ ᱜᱮᱞ ᱮᱭᱟᱭ ᱫᱚ ᱡᱚᱛᱚ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱮᱞ ᱠᱟᱱᱟ, ᱟᱨ ᱱᱚᱣᱟ ᱫᱚ ᱦᱚᱲ ᱵᱟᱵᱚᱛ ᱨᱮᱭᱟᱜ ᱠᱟᱛᱷᱟ ᱠᱟᱱᱟ᱾
ᱜᱚᱱᱤᱛ ᱥᱟᱶ ᱨᱟᱹᱥᱠᱟᱹ
ᱱᱚᱶᱟ ᱠᱚ ᱯᱩᱭᱞᱩ ᱟᱯᱮ ᱛᱮ ᱠᱩᱨᱩᱢᱩᱴᱩ ᱯᱮ᱾ ᱢᱤᱫ ᱢᱤᱫ ᱥᱚᱢᱟᱫᱷᱟᱱ ᱫᱚ ᱩᱠᱩ ᱢᱮᱱᱟᱜ-ᱟ; ᱛᱮᱭᱟᱨ ᱦᱩᱭ ᱠᱟᱛᱮ ᱡᱷᱤᱡᱽ ᱯᱮ᱾
ᱟᱯᱮ ᱡᱚᱛᱚ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣ ᱮᱫᱟ ᱯᱮ᱾ ᱟᱯᱮᱭᱟᱜ ᱢᱚᱬᱮ ᱱᱚᱢᱵᱚᱨ ᱡᱤᱛ ᱴᱷᱤᱠ ᱤᱨᱟᱹᱞ ᱱᱚᱢᱵᱚᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱦᱤᱡᱩᱜ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ ᱪᱮᱫ? ᱟᱨ ᱯᱟᱦᱤᱞ ᱤᱨᱟᱹᱞ ᱜᱷᱩᱨᱟᱹᱣ ᱵᱷᱤᱛᱤᱨ ᱨᱮ ᱢᱚᱬᱮ ᱡᱤᱛ ᱧᱟᱢ ᱨᱮᱭᱟᱜ?
ᱥᱚᱢᱟᱫᱷᱟᱱ ᱩᱫᱩᱜ
ᱛᱮᱞᱟ ᱤᱨᱟᱹᱞ ᱱᱚᱢᱵᱚᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱚᱬᱮ ᱱᱚᱢᱵᱚᱨ ᱡᱤᱛ ᱞᱟᱹᱜᱤᱫ 12.9%, ᱡᱟᱦᱟᱱ 8 ᱨᱮ 1᱾ ᱚᱱᱟ ᱦᱟᱹᱵᱤᱡ ᱢᱚᱬᱮ ᱡᱤᱛ ᱞᱟᱹᱜᱤᱫ 33.4%᱾
ᱤᱨᱟᱹᱞ ᱱᱚᱢᱵᱚᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱚᱬᱮ ᱱᱚᱢᱵᱚᱨ ᱡᱤᱛ ᱢᱮᱱᱮᱛᱮ ᱵᱟᱨ ᱡᱤᱱᱤᱥ: ᱤᱨᱟᱹᱞ ᱱᱚᱢᱵᱚᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱡᱤᱛᱟᱹᱣᱚᱜ-ᱟ, ᱟᱨ ᱯᱟᱦᱤᱞ ᱮᱭᱟᱭ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱴᱷᱤᱠ ᱯᱩᱱ ᱡᱤᱛ ᱟᱨ ᱯᱮ ᱦᱟᱹᱱᱤ ᱢᱮᱱᱟᱜ-ᱟ, ᱡᱟᱦᱟᱸ ᱦᱚᱸ ᱛᱟᱨᱛᱤᱵ ᱛᱮ᱾ ᱮᱭᱟᱭ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱯᱩᱱ ᱡᱤᱛ ᱫᱚᱦᱚ ᱞᱟᱹᱜᱤᱫ 35 ᱞᱮᱠᱟ ᱢᱮᱱᱟᱜ-ᱟ᱾
ᱚᱱᱟᱛᱮ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱫᱚ 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%᱾
ᱤᱨᱟᱹᱞ ᱱᱚᱢᱵᱚᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱦᱟᱹᱵᱤᱡ ᱢᱚᱬᱮ ᱡᱤᱛ ᱞᱟᱹᱜᱤᱫ, ᱢᱚᱬᱮ, ᱛᱩᱨᱩᱭ ᱟᱨ ᱮᱭᱟᱭ ᱱᱚᱢᱵᱚᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱚᱬᱮ ᱱᱚᱢᱵᱚᱨ ᱡᱤᱛ ᱨᱮᱭᱟᱜ ᱚᱱᱟ ᱞᱮᱠᱟᱱ ᱦᱟᱹᱴᱤᱧ ᱡᱚᱲᱟᱣ ᱯᱮ: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%᱾ ᱥᱴᱮᱴᱤᱥᱴᱤᱠᱥ ᱵᱟᱰᱟᱭᱤᱭᱟᱹ ᱠᱚ ᱱᱚᱣᱟ ᱫᱚ ᱱᱮᱜᱮᱴᱤᱵᱷ ᱵᱟᱭᱱᱚᱢᱤᱭᱟᱞ ᱵᱟᱸᱴᱟᱣ ᱠᱚ ᱢᱮᱱᱟ: ᱢᱤᱫ ᱴᱷᱤᱠ ᱞᱮᱠᱷᱟ ᱥᱟᱯᱷᱟᱞ ᱞᱟᱹᱜᱤᱫ ᱛᱤᱱᱟᱹᱜ ᱠᱩᱨᱩᱢᱩᱴᱩ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾ ᱴᱮᱞᱟᱨ (Taylor, 2021) ᱚᱱᱟ ᱜᱮ ᱠᱩᱠᱞᱤ ᱟᱢᱮᱨᱤᱠᱟᱱ ᱪᱟᱠᱟ ᱨᱮ ᱮ ᱦᱤᱥᱟᱹᱵ ᱟᱠᱟᱫᱟ, 12.2%᱾
ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ
ᱠᱷᱟᱱᱟ ᱞᱮᱠᱷᱟ ᱯᱮ᱾ 37 ᱛᱮ ᱦᱟᱹᱴᱤᱧ ᱯᱮ᱾ ᱞᱟᱹᱲᱤ ᱞᱟᱹᱜᱤᱫ ᱜᱩᱱ ᱯᱮ᱾ ᱦᱩᱭ ᱮᱱᱟ᱾
ᱯᱷᱮᱰᱟᱛ
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.
- Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed.