ᱨᱩᱞᱮᱴ ᱜᱚᱱᱤᱛ · ᱜᱚᱱᱤᱛ ᱥᱚᱢᱥᱭᱟ · 7 ᱢᱤᱱᱤᱴ

ᱥᱚᱢᱥᱭᱟ: ᱡᱤᱨᱚ ᱦᱟᱹᱵᱤᱡ ᱪᱮᱫᱟᱜ ᱡᱮᱞᱮᱧ

Q: ᱪᱮᱫ ᱠᱚᱭᱢᱟ ᱪᱟᱠᱟ ᱨᱮ ᱡᱤᱨᱚ ᱵᱮᱥᱤ ᱦᱤᱡᱩᱜ-ᱟ?

ᱴᱷᱤᱠ ᱪᱟᱠᱟ ᱨᱮ ᱫᱚ ᱵᱟᱝ᱾ ᱵᱟᱭᱟᱥ ᱪᱟᱠᱟ ᱨᱮ ᱡᱟᱦᱟᱱᱟᱜ ᱠᱷᱟᱱᱟ ᱦᱚᱸ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱟᱨ ᱚᱱᱟ ᱵᱟᱰᱟᱭ ᱞᱟᱹᱜᱤᱫ ᱦᱟᱡᱟᱨ ᱦᱟᱡᱟᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾

ᱡᱤᱨᱚ ᱫᱚ ᱟᱣᱥᱚᱛ ᱛᱮ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱢᱤᱫ ᱫᱷᱟᱣ ᱦᱤᱡᱩᱜ-ᱟ᱾ ᱥᱟᱹᱨᱤ ᱛᱮ ᱛᱤᱱᱟᱹᱜ ᱚᱠᱛᱚ ᱟᱹᱛᱩᱨ ᱦᱩᱭᱩᱜ-ᱟ, ᱟᱨ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱤᱡ ᱞᱟᱹᱜᱤᱫ ᱚᱱᱟ ᱪᱮᱫ ᱠᱟᱹᱢᱤᱭᱟ?

ᱠᱷᱟᱴᱚ ᱛᱮᱞᱟ

ᱡᱤᱨᱚ ᱨᱮᱭᱟᱜ ᱟᱹᱛᱩᱨ ᱫᱚ ᱡᱤᱭᱚᱢᱮᱴᱨᱤᱠ: ᱟᱣᱥᱚᱛ 37 ᱜᱷᱩᱨᱟᱹᱣ, ᱢᱤᱰᱤᱭᱟᱱ 25, ᱟᱨ ᱵᱟᱨ ᱜᱮᱞ ᱟᱹᱛᱩᱨ ᱨᱮ ᱢᱤᱫ ᱫᱚ 110 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱚᱱ ᱵᱮᱥᱤ᱾ 200 ᱜᱷᱩᱨᱟᱹᱣ ᱥᱮᱥᱚᱱ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱤᱡ ᱫᱚ 5.4 ᱡᱤᱨᱚ ᱟᱸᱫᱟᱡᱽ ᱮ ᱫᱚᱦᱚᱭᱟ ᱟᱨ 1 ᱠᱷᱚᱱ 10 ᱦᱟᱹᱵᱤᱡ ᱡᱟᱦᱟᱸ ᱦᱚᱸ ᱮ ᱧᱮᱞ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾

ᱟᱣᱥᱚᱛ ᱟᱹᱛᱩᱨ

37 ᱜᱷᱩᱨᱟᱹᱣ

ᱢᱤᱰᱤᱭᱟᱱ ᱟᱹᱛᱩᱨ

25 ᱜᱷᱩᱨᱟᱹᱣ

p(100 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱤᱨᱚ ᱵᱟᱹᱱᱩᱜ)

6.5%

200 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱤᱨᱚ

5.4 ± 2.3

ᱥᱚᱢᱥᱭᱟ

ᱡᱤᱨᱚᱪᱟᱠᱟᱡᱤᱨᱚᱢᱤᱫᱜᱮ ᱦᱟᱹᱨᱭᱟᱹᱲ ᱠᱷᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ, ᱰᱚᱡᱮᱱ ᱟᱨᱵᱟᱝ ᱠᱚᱞᱚᱢ ᱵᱟᱡᱤ ᱵᱟᱭ ᱠᱚᱵᱷᱟᱨᱟ; ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱨᱮᱭᱟᱜ ᱢᱩᱞ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱤᱝᱜᱚᱞ ᱡᱤᱨᱚ, 0᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟᱜᱚᱱᱤᱛᱥᱚᱢᱵᱷᱟᱵᱱᱟᱢᱤᱫ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ, 0 ᱠᱷᱚᱱ 1 ᱟᱨᱵᱟᱝ 0% ᱠᱷᱚᱱ 100%᱾ ᱢᱤᱫ ᱮᱞ: 1/37 = 2.70%᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱫᱚ ᱢᱤᱫ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 1/37᱾ (a) ᱫᱟᱨᱟᱭ 37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱤᱨᱚ ᱵᱟᱹᱱᱩᱜ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱤᱱᱟᱹᱜ? (b) ᱢᱤᱰᱤᱭᱟᱱ ᱟᱹᱛᱩᱨ ᱛᱤᱱᱟᱹᱜ? (c) 200 ᱜᱷᱩᱨᱟᱹᱣ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱥᱮᱥᱚᱱ ᱨᱮ ᱠᱷᱮᱞᱚᱸᱰ ᱫᱚ ᱛᱤᱱᱟᱹᱜ ᱡᱤᱨᱚ ᱟᱸᱫᱟᱡᱽ ᱞᱟᱹᱠᱛᱤᱭᱟ, ᱟᱨ ᱯᱟᱥᱱᱟᱣ ᱫᱚ ᱛᱤᱱᱟᱹᱜ?

ᱥᱟᱢᱵᱷᱟᱲ

(a) (36/37)³⁷ = 36.3%᱾ ᱯᱮ ᱦᱟᱹᱴᱤᱧ ᱨᱮᱭᱟᱜ ᱢᱤᱫ ᱦᱟᱹᱴᱤᱧ ᱠᱷᱚᱱ ᱵᱮᱥᱤ ᱚᱠᱛᱚ, 37 ᱜᱷᱩᱨᱟᱹᱣ ᱫᱚ ᱢᱤᱫ ᱡᱤᱨᱚ ᱵᱮᱜᱚᱨ ᱜᱮ ᱪᱟᱞᱟᱜ-ᱟ; ᱱᱚᱶᱟ ᱫᱚ ᱚᱱᱟ ᱜᱮ ᱦᱤᱥᱟᱹᱵ ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱛᱮ “37 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱥᱴᱨᱮᱴ ᱚᱯᱵᱟᱡᱤᱥᱴᱨᱮᱴ ᱚᱯᱢᱤᱫ ᱮᱞ, ᱵᱷᱩᱜᱛᱟᱱ 35:1᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱠᱚᱢ ᱥᱮ ᱠᱚᱢ ᱢᱤᱫ ᱦᱤᱴ” ᱫᱚ ᱠᱷᱟᱹᱞᱤ 63.7%᱾ (b) ᱟᱹᱛᱩᱨ W ᱫᱚ ᱡᱤᱭᱚᱢᱮᱴᱨᱤᱠ; p(W > k) = (36/37)ᵏ; ᱢᱤᱰᱤᱭᱟᱱ ᱫᱚ ᱚᱱᱟ k ᱠᱟᱱᱟ ᱡᱟᱦᱟᱸ ᱨᱮ ᱱᱚᱶᱟ 0.5 ᱯᱟᱨᱚᱢᱚᱜ-ᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ k ≈ 25᱾ ᱟᱫᱷᱟ ᱟᱹᱛᱩᱨ ᱫᱚ 25 ᱜᱷᱩᱨᱟᱹᱣ ᱥᱮ ᱠᱚᱢ ᱟᱨ ᱟᱫᱷᱟ ᱫᱚ ᱵᱮᱥᱤ; 37 ᱟᱣᱥᱚᱛ ᱫᱚ ᱡᱮᱞᱮᱧ ᱪᱮᱞᱚᱢ ᱛᱮ ᱪᱮᱛᱟᱱ ᱟᱹᱜᱩ ᱟᱠᱟᱱᱟ᱾ (c) 200 ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱤᱨᱚ ᱫᱚ ᱵᱟᱭᱱᱚᱢᱤᱭᱟᱞ, ᱟᱣᱥᱚᱛ 200/37 = 5.4 ᱟᱨ ᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱜᱚᱱᱤᱛᱥᱴᱮᱱᱰᱟᱨᱰ ᱰᱤᱵᱷᱤᱭᱮᱥᱚᱱᱣᱮᱨᱤᱭᱮᱱᱥ ᱨᱮᱭᱟᱜ ᱵᱚᱜᱚ ᱢᱩᱞ; ᱟᱸᱫᱟᱡᱽ ᱜᱚᱱᱚᱝ ᱠᱷᱚᱱ ᱨᱮᱡᱟᱞᱴ ᱨᱮᱭᱟᱜ ᱥᱟᱫᱷᱟᱨᱚᱱ ᱥᱟᱦᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → √(200 × (1/37) × (36/37)) ≈ 2.3᱾ 95% ᱯᱟᱥᱱᱟᱣ ᱫᱚ ᱠᱚᱢ ᱵᱮᱥᱤ 1 ᱠᱷᱚᱱ 10 ᱦᱟᱹᱵᱤᱡ᱾

ᱡᱤᱨᱚ ᱨᱮᱭᱟᱜ ᱟᱹᱛᱩᱨᱥᱚᱢᱵᱷᱟᱵᱱᱟ

10 ᱜᱷᱩᱨᱟᱹᱣ ᱵᱷᱤᱛᱤᱨ24.0%

25 ᱜᱷᱩᱨᱟᱹᱣ ᱵᱷᱤᱛᱤᱨ49.6%

37 ᱜᱷᱩᱨᱟᱹᱣ ᱵᱷᱤᱛᱤᱨ63.7%

50 ᱜᱷᱩᱨᱟᱹᱣ ᱵᱷᱤᱛᱤᱨ74.6%

100 ᱜᱷᱩᱨᱟᱹᱣ ᱵᱷᱤᱛᱤᱨ93.5%

110 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱚᱱ ᱵᱮᱥᱤ≈ 5%

200 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱷᱚᱱ ᱵᱮᱥᱤ0.4%

p(W ≤ k) = 1 − (36/37)ᵏ᱾ ᱟᱣᱥᱚᱛ 37, ᱢᱤᱰᱤᱭᱟᱱ 25᱾

ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱤᱡ ᱞᱟᱹᱜᱤᱫ ᱡᱤᱨᱚ ᱨᱮᱭᱟᱜ ᱠᱷᱚᱨᱚᱪ

ᱡᱚᱛᱚ ᱡᱤᱨᱚ ᱫᱚ ᱢᱤᱫ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱦᱟᱨᱟᱣᱟ, ᱟᱨ ᱟᱨᱟᱜᱵᱟᱡᱤᱟᱨᱟᱜ18 ᱟᱨᱟᱜ ᱮᱞ ᱨᱮ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ᱾ ᱯᱷᱨᱮᱧᱪ ᱨᱮ: ᱨᱩᱡᱽ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱥᱟᱱᱟᱢ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱫᱚ ᱡᱤᱨᱚ ᱜᱮ ᱠᱟᱱᱟ: 37 ᱟᱣᱥᱚᱛ ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ 18 ᱡᱤᱛ ᱟᱨ 18 ᱦᱟᱹᱱᱤ ᱥᱚᱢᱟᱱᱚᱜ-ᱟ, ᱟᱨ ᱢᱤᱫ ᱡᱤᱨᱚ ᱫᱚ −1/37 ᱠᱟᱱᱟ᱾ $10 ᱛᱮ 200 ᱜᱷᱩᱨᱟᱹᱣ ᱥᱮᱥᱚᱱ ᱨᱮ ᱟᱸᱫᱟᱡᱽ 5.4 ᱡᱤᱨᱚ ᱫᱚ $54 ᱠᱷᱚᱨᱚᱪ ᱮᱢᱟ, ᱡᱟᱦᱟᱸ ᱫᱚ ᱴᱷᱤᱠ 200 × $10 / 37᱾ 2 ᱡᱤᱨᱚ ᱥᱮᱥᱚᱱ ᱨᱮ $34 ᱨᱮᱭᱟᱜ ᱵᱷᱟᱜᱚ ᱵᱷᱟᱹᱜᱤ ᱦᱩᱭ ᱞᱮᱱᱟ; 9 ᱡᱤᱨᱚ ᱥᱮᱥᱚᱱ ᱨᱮ $36 ᱨᱮᱭᱟᱜ ᱵᱟᱹᱲᱤᱡ ᱵᱷᱟᱹᱜᱤ, ᱟᱨ ᱚᱱᱟ ᱫᱚ ᱪᱟᱞᱟᱠ ᱞᱮᱠᱟ ᱟᱹᱭᱠᱟᱹᱣᱚᱜ-ᱟ᱾ ᱞᱟ ᱯᱟᱨᱛᱟᱡᱽᱱᱤᱭᱚᱢᱞᱟ ᱯᱟᱨᱛᱟᱡᱽᱯᱷᱨᱮᱧᱪ ᱱᱤᱭᱚᱢ: ᱡᱤᱨᱚ ᱦᱤᱡᱩᱜ ᱞᱮᱠᱷᱟᱱ ᱥᱚᱢᱟᱱ ᱴᱟᱠᱟ ᱵᱟᱡᱤ ᱨᱮᱭᱟᱜ ᱟᱫᱷᱟ ᱨᱩᱣᱟᱹᱲᱚᱜ-ᱟ᱾ ᱚᱱᱟ ᱵᱟᱡᱤ ᱠᱚ ᱨᱮ ᱠᱮᱥᱤᱱᱳ ᱵᱟᱲᱛᱤ ᱟᱫᱷᱟ, 1.35% ᱦᱩᱭᱩᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱴᱮᱵᱩᱞ ᱨᱮ ᱡᱚᱛᱚ ᱡᱤᱨᱚ ᱫᱚ ᱟᱫᱷᱟ ᱵᱟᱡᱤ ᱴᱟᱠᱟ ᱦᱟᱨᱟᱣᱟ ᱟᱨ ᱮᱞ ᱠᱚ ᱟᱫᱷᱟ ᱦᱩᱭᱩᱜ-ᱟ᱾

200 ᱜᱷᱩᱨᱟᱹᱣ ᱥᱮᱥᱚᱱ ᱨᱮ ᱡᱤᱨᱚᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ %

0–1

2.5%

2–3

18%

4–5

34%

6–7

28%

8–9

13%

10 ᱥᱮ ᱵᱮᱥᱤ

4.5%

ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ %

01734%

ᱵᱟᱭᱱᱚᱢᱤᱭᱟᱞ(200, 1/37)᱾ $10 ᱟᱨᱟᱜ ᱵᱟᱡᱤ ᱞᱟᱜᱟᱣᱤᱡ ᱫᱚ ᱡᱚᱛᱚ ᱡᱤᱨᱚ ᱨᱮ $10 ᱮ ᱮᱢᱟ; ᱡᱤᱨᱚ ᱨᱮᱭᱟᱜ ᱯᱟᱥᱱᱟᱣ ᱫᱚ ᱧᱤᱫᱟᱹ ᱨᱮᱭᱟᱜ ᱫᱟᱢ ᱨᱮᱭᱟᱜ ᱯᱟᱥᱱᱟᱣ ᱠᱟᱱᱟ᱾

ᱞᱟ ᱯᱟᱨᱛᱟᱡᱽ ᱨᱩᱞᱮᱴ ᱱᱤᱭᱚᱢ ᱚᱱᱞᱟᱭᱤᱱ ᱨᱩᱞᱮᱴ ᱨᱮ ᱠᱷᱚᱞ ᱢᱮᱱᱟᱜ-ᱟ ᱥᱮ? ᱵᱷᱨᱚᱢ

ᱫᱟᱨᱟᱭ ᱥᱚᱢᱥᱭᱟ

ᱞᱟᱜᱟᱛᱟᱨ ᱵᱟᱨ ᱡᱤᱨᱚ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ ᱛᱤᱱᱟᱹᱜ? (1/37)² = 1/1,369᱾ 20 ᱴᱮᱵᱩᱞ ᱨᱮ ᱢᱤᱫ ᱜᱷᱟᱸᱴᱟ ᱨᱮ 50 ᱜᱷᱩᱨᱟᱹᱣ ᱪᱟᱞᱟᱣᱤᱡ ᱠᱮᱥᱤᱱᱳ ᱨᱮ, ᱚᱱᱟ ᱫᱚ ᱡᱚᱛᱚ 1.4 ᱜᱷᱟᱸᱴᱟ ᱨᱮ ᱡᱟᱦᱟᱸ ᱜᱮ ᱴᱷᱟᱶ ᱨᱮ ᱠᱚᱢ ᱵᱮᱥᱤ ᱢᱤᱫ ᱡᱚᱲᱟ ᱞᱟᱜᱟᱛᱟᱨ ᱡᱤᱨᱚ᱾ ᱱᱚᱶᱟ ᱧᱮᱞ ᱠᱷᱮᱞᱚᱸᱰ ᱠᱚ ᱵᱷᱟᱵᱱᱟ ᱠᱚ ᱡᱮ ᱪᱟᱠᱟ ᱫᱚ ᱨᱟᱯᱩᱫ ᱟᱠᱟᱱᱟ; ᱦᱤᱥᱟᱹᱵ ᱫᱚ ᱢᱮᱱᱟᱜ-ᱟ ᱡᱮ ᱱᱚᱶᱟ ᱫᱚ ᱥᱟᱫᱷᱟᱨᱚᱬ ᱢᱚᱝᱜᱚᱞ ᱢᱟᱦᱟᱸ ᱜᱮ᱾

ᱪᱮᱥᱴᱟ ᱯᱮ

ᱨᱩᱞᱮᱴ ᱥᱮᱥᱚᱱ ᱥᱤᱢᱩᱞᱮᱴᱚᱨ ᱫᱚ ᱡᱚᱛᱚ ᱥᱮᱥᱚᱱ ᱨᱮ ᱡᱤᱨᱚ ᱮ ᱞᱮᱠᱷᱟᱭᱟ᱾ 100 ᱜᱷᱩᱨᱟᱹᱣ ᱠᱚᱭᱢᱟ ᱥᱟᱭ ᱫᱷᱟᱣ ᱪᱟᱞᱟᱣ ᱯᱮ ᱟᱨ ᱞᱮᱠᱷᱟ ᱨᱮᱭᱟᱜ ᱪᱤᱛᱟᱹᱨ ᱵᱮᱱᱟᱣ ᱯᱮ: ᱪᱮᱛᱟᱱ ᱨᱮᱭᱟᱜ ᱦᱤᱥᱴᱚᱜᱽᱨᱟᱢ ᱫᱚ ᱩᱫᱩᱜᱚᱜ-ᱟ, ᱟᱡᱟᱜ ᱡᱮᱞᱮᱧ ᱡᱚᱡᱚᱢ ᱪᱮᱞᱚᱢ ᱥᱟᱶ᱾ ᱠᱟᱹᱦᱱᱤ ᱠᱚ ᱫᱚ ᱚᱱᱟ ᱪᱮᱞᱚᱢ ᱠᱷᱚᱱ ᱜᱮ ᱦᱮᱡᱚᱜ-ᱟ᱾

ᱯᱷᱚᱨᱢᱩᱞᱟ

p(W > k) = (36/37)ᵏ

E[W] = 37 · ᱢᱤᱰᱤᱭᱟᱱ ≈ 25

N ᱜᱷᱩᱨᱟᱹᱣ ᱨᱮ ᱡᱤᱨᱚ ~ ᱵᱟᱭᱱᱚᱢᱤᱭᱟᱞ(N, 1/37)

ᱠᱩᱠᱞᱤ ᱠᱚ

ᱪᱮᱫ ᱠᱚᱭᱢᱟ ᱪᱟᱠᱟ ᱨᱮ ᱡᱤᱨᱚ ᱵᱮᱥᱤ ᱦᱤᱡᱩᱜ-ᱟ?

ᱴᱷᱤᱠ ᱪᱟᱠᱟ ᱨᱮ ᱫᱚ ᱵᱟᱝ᱾ ᱵᱟᱭᱟᱥ ᱪᱟᱠᱟᱞᱮᱵᱵᱟᱭᱟᱥ ᱪᱟᱠᱟᱢᱤᱫ ᱪᱟᱠᱟ ᱡᱟᱦᱟᱸ ᱨᱮᱭᱟᱜ ᱦᱟᱛ ᱫᱚᱥ ᱛᱮ ᱛᱤᱱᱟᱹᱜ ᱜᱟᱱ ᱠᱷᱟᱱᱟ ᱨᱮᱭᱟᱜ ᱥᱚᱢᱵᱷᱟᱵᱱᱟ 1/37 ᱠᱷᱚᱱ ᱵᱟᱹᱲᱛᱤ᱾ ᱟᱹᱰᱤ ᱠᱚᱢ ᱧᱟᱢᱚᱜ-ᱟ, ᱦᱟᱡᱟᱨ ᱦᱟᱡᱟᱨ ᱚᱞ ᱟᱠᱟᱱ ᱜᱷᱩᱨᱟᱹᱣ ᱛᱮ ᱜᱮ ᱧᱟᱢ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱨᱮ ᱡᱟᱦᱟᱱᱟᱜ ᱠᱷᱟᱱᱟᱥᱟᱡ ᱥᱟᱢᱟᱱᱠᱷᱟᱱᱟᱨᱚᱴᱚᱨ ᱨᱮᱭᱟᱜ 37 ᱮᱞ ᱚᱞ ᱠᱷᱟᱱᱟ ᱠᱷᱚᱱ ᱢᱤᱫ᱾ ᱮᱴᱟᱜ ᱧᱩᱛᱩᱢ: ᱥᱞᱚᱴ, ᱠᱟᱯ᱾ᱯᱩᱨᱟᱹ ᱯᱟᱲᱦᱟᱣ → ᱦᱚᱸ ᱦᱩᱭ ᱫᱟᱲᱮᱭᱟᱜ-ᱟ, ᱟᱨ ᱚᱱᱟ ᱵᱟᱰᱟᱭ ᱞᱟᱹᱜᱤᱫ ᱦᱟᱡᱟᱨ ᱦᱟᱡᱟᱨ ᱜᱷᱩᱨᱟᱹᱣ ᱞᱟᱹᱠᱛᱤᱭᱟ᱾

ᱵᱤᱢᱟ ᱞᱮᱠᱟᱛᱮ ᱤᱧ ᱡᱚᱛᱚ ᱚᱠᱛᱚ ᱡᱤᱨᱚ ᱨᱮ ᱢᱤᱫ ᱪᱤᱯ ᱫᱚᱦᱚ ᱞᱟᱹᱠᱛᱤᱭᱟ ᱥᱮ?

ᱚᱱᱟ ᱦᱚᱸ ᱮᱴᱟᱜ ᱡᱚᱛᱚ ᱞᱮᱠᱟ ᱜᱮ 2.70% ᱵᱟᱡᱤ ᱠᱟᱱᱟ᱾ ᱚᱱᱟ ᱫᱚ ᱥᱮᱥᱚᱱ ᱨᱮᱭᱟᱜ ᱨᱩᱯ ᱵᱚᱫᱚᱞᱟ (ᱡᱤᱨᱚ ᱫᱚ ᱡᱤᱛ ᱦᱩᱭᱩᱜ-ᱟ), ᱠᱷᱚᱨᱚᱪ ᱫᱚ ᱵᱟᱝ᱾

ᱢᱤᱰᱤᱭᱟᱱ ᱫᱚ ᱟᱣᱥᱚᱛ ᱠᱷᱚᱱ ᱪᱮᱫᱟᱜ ᱠᱚᱢ?

ᱪᱮᱫᱟᱜ ᱥᱮ ᱟᱹᱛᱩᱨ ᱨᱮᱭᱟᱜ ᱵᱟᱸᱴᱟᱣ ᱫᱚ ᱮᱠᱷᱤᱡ ᱥᱮᱫ ᱜᱷᱟᱸᱡᱟᱣ ᱟᱠᱟᱱᱟ: ᱟᱭᱢᱟ ᱦᱩᱰᱤᱧ ᱟᱹᱛᱩᱨ, ᱠᱚᱭᱢᱟ ᱟᱹᱰᱤ ᱡᱮᱞᱮᱧ᱾

ᱞᱟᱸᱫᱟ ᱞᱟᱹᱜᱤᱫ ᱠᱚᱢᱤᱠ

$ᱟᱣᱥᱚᱛ 37, ᱢᱤᱰᱤᱭᱟᱱ 25, ᱟᱨ ᱢᱤᱫ ᱡᱮᱞᱮᱧ ᱪᱮᱞᱚᱢ ᱡᱟᱦᱟᱸ ᱨᱮ ᱠᱟᱹᱦᱱᱤ ᱠᱚ ᱛᱟᱦᱮᱸᱱᱟ᱾$

ᱟᱣᱥᱚᱛ 37, ᱢᱤᱰᱤᱭᱟᱱ 25, ᱟᱨ ᱢᱤᱫ ᱡᱮᱞᱮᱧ ᱪᱮᱞᱚᱢ ᱡᱟᱦᱟᱸ ᱨᱮ ᱠᱟᱹᱦᱱᱤ ᱠᱚ ᱛᱟᱦᱮᱸᱱᱟ᱾

ᱯᱷᱮᱰᱟᱛ

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3 ᱥᱚᱝᱥᱠᱟᱨᱚᱬ, 1968᱾ ᱡᱩᱣᱟᱲᱤ ᱨᱮᱭᱟᱜ ᱯᱩᱸᱡᱤ ᱢᱩᱪᱟᱹᱫ, ᱪᱮᱯᱴᱟᱨ XIV᱾
Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010᱾ ᱪᱮᱯᱴᱟᱨ 13, ᱨᱩᱞᱮᱴ᱾

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