ꯔꯨꯂꯦꯠꯀꯤ ꯃꯦꯊꯃꯦꯇꯤꯛꯁ · ꯃꯔꯨꯑꯣꯏꯕ ꯋꯥꯈꯜꯂꯣꯟ · ꯃꯤꯅꯤꯠ 8

ꯔꯨꯂꯦꯠꯀꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ

ꯔꯨꯂꯦꯠꯀꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯈꯨꯗꯤꯡꯃꯛ ꯄꯣꯀꯦꯠ ꯀꯌꯥ ꯂꯩꯕꯒꯦ ꯍꯥꯌꯕꯗꯨ 37 ꯅ ꯌꯦꯟꯊꯣꯀꯄꯅꯤ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

p = ꯀꯨꯞꯄ ꯃꯁꯤꯡꯁꯤꯡ / 37꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 2.70%꯫ ꯃꯁꯤꯡ ꯇꯔꯥꯅꯤꯄꯥꯟ: 48.65%꯫ ꯑꯀꯛꯅꯕ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯃꯊꯪ ꯃꯊꯪꯒꯤ ꯊꯣꯛꯄ ꯑꯃꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯗꯤ ꯁ꯭ꯄꯤꯟ ꯑꯃꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯁꯤꯡ ꯃꯔꯥꯡ ꯀꯥꯏꯕꯅꯤ꯫

ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ
1/37 · 2.70%
ꯗꯖꯟ
12/37 · 32.43%
ꯆꯞ ꯃꯥꯟꯅꯕ
18/37 · 48.65%
ꯑꯉꯥꯡꯕ ꯑꯅꯤ
23.67%

ꯁ꯭ꯄꯤꯟ ꯑꯃꯈꯛ

ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 37 ꯈꯨꯗꯤꯡꯃꯛꯇ ꯕꯣꯜ ꯂꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯃꯥꯟꯅꯩ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯔꯨꯂꯦꯠꯇ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ ꯃꯁꯤꯡ ꯊꯤꯕꯒꯤ ꯋꯥꯐꯃꯈꯛꯅꯤ꯫ ꯃꯁꯤꯡ ꯃꯔꯤꯗ ꯊꯝꯕ ꯕꯦꯠ ꯑꯃꯅ ꯃꯇꯃꯒꯤ 4/37, 10.8% ꯃꯔꯛ, ꯃꯥꯏꯄꯥꯛꯏ꯫ ꯁ꯭ꯄꯤꯟ ꯑꯃꯒꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯗ ꯃꯁꯤꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯀꯔꯤꯁꯨ ꯂꯩꯇꯦ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯁꯥꯟꯅꯕ ꯄꯨꯝꯅꯃꯛ ꯅꯦꯞꯀꯤꯟ ꯑꯃꯗ ꯏꯗꯨꯅ ꯊꯤꯖꯤꯟꯕ ꯌꯥꯏ꯫

ꯕꯦꯠ ꯃꯈꯜ ꯃꯈꯜꯒꯤ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯁ꯭ꯄꯤꯟꯁꯤꯡꯒꯤ %
ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ (1)
2.70%
ꯁ꯭ꯞꯂꯤꯠ (2)
5.41%
ꯁ꯭ꯇ꯭ꯔꯤꯠ (3)
8.11%
ꯀꯣꯔꯅꯔ (4)
10.81%
ꯁꯤꯛꯁ ꯂꯥꯏꯟ (6)
16.22%
ꯗꯖꯟ / ꯀꯂꯝ (12)
32.43%
ꯆꯞ ꯃꯥꯟꯅꯕ (18)
48.65%
ꯁ꯭ꯄꯤꯟꯁꯤꯡꯒꯤ %
024.3248.65%
ꯕꯦꯠ ꯈꯨꯗꯤꯡꯃꯛ ꯀꯨꯞꯄ ꯃꯁꯤꯡꯁꯤꯡꯕꯨ 37 ꯅ ꯌꯦꯟꯊꯣꯀꯄꯅꯤ꯫ ꯀꯨꯞꯄ ꯍꯦꯅꯒꯠꯂꯀꯄꯒ ꯂꯣꯌꯅꯅ ꯄꯦꯑꯥꯎꯠ ꯍꯟꯊꯔꯛꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯂꯥꯏꯟ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯐꯪꯒꯗꯕ ꯃꯃꯜ ꯑꯗꯨ −2.70% ꯃꯥꯟꯅꯩ꯫

ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ

ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯃꯔꯤ ꯂꯩꯅꯗꯦ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯊꯪ ꯃꯊꯪꯒꯤ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯁꯤꯡ ꯃꯔꯥꯡ ꯀꯥꯏꯏ꯫ ꯃꯈꯥ ꯆꯠꯅꯅ ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯅꯤ: (18/37)² = 23.7%꯫ ꯑꯉꯥꯡꯕ ꯑꯃꯁꯨꯡ ꯃꯇꯨꯡꯗ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →: (18/37)(1/37) = 1.3%꯫ ꯃꯈꯥ ꯆꯠꯅꯅ ꯇꯔꯥꯇꯔꯦꯠ ꯑꯃꯨꯛ ꯑꯅꯤ: (1/37)² = 0.073%, 1,369 ꯗꯒꯤ ꯑꯃꯥ ꯃꯔꯛ꯫ ꯑꯀꯛꯅꯕ ꯃꯊꯪ ꯃꯊꯪꯒꯤꯗꯃꯛ ꯂꯥꯛꯄꯒꯤ ꯃꯊꯪ ꯃꯊꯪ ꯑꯗꯨ ꯃꯔꯨ ꯑꯣꯏ, ꯃꯁꯤꯡ ꯊꯤꯕꯗꯗꯤ ꯃꯔꯨ ꯑꯣꯏꯗꯦ: “ꯑꯉꯥꯡꯕ ꯑꯃꯁꯨꯡ ꯃꯇꯨꯡꯗ ꯑꯃꯨꯕꯕꯦꯠꯑꯃꯨꯕꯑꯃꯨꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯅꯣꯌꯥꯔ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →” ꯑꯁꯤ 25.0% ꯅꯤ, ꯑꯗꯨꯕꯨ “ꯁ꯭ꯄꯤꯟ ꯑꯅꯤꯗ ꯑꯉꯥꯡꯕ ꯑꯃꯥ ꯑꯃꯁꯨꯡ ꯑꯃꯨꯕ ꯑꯃꯥ, ꯀꯔꯤꯒꯨꯝꯕ ꯃꯊꯪ ꯃꯊꯪꯗ” ꯑꯁꯤ 50.0% ꯅꯤ꯫

ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯔꯨꯂꯦꯠ ꯁ꯭ꯄꯤꯟꯁꯤꯡ

ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯑꯃꯨꯛ

ꯑꯣꯟꯊꯣꯛꯂꯕ ꯃꯍꯩ (ꯀꯝꯞ꯭ꯂꯤꯃꯦꯟꯠ) ꯁꯤꯖꯤꯟꯅꯕꯤꯌꯨ꯫ ꯁ꯭ꯄꯤꯟ 37 ꯗ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯕꯦꯠꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞꯃꯁꯤꯡ ꯑꯃꯈꯛꯇ, 35:1 ꯄꯦꯑꯥꯎꯠ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯠꯇ ꯃꯥꯏꯄꯥꯛꯇꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ (36/37)³⁷ = 36.3% ꯅꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯑꯃꯨꯛ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 63.7% ꯅꯤ, 37 ꯗꯒꯤ 1 ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 37 ꯐꯪꯂꯕꯗ ꯁꯥꯟꯅꯔꯤꯕ ꯀꯌꯥꯅ ꯊꯥꯖꯕ “ꯁꯣꯏꯗꯅ” ꯅꯠꯇꯦ꯫ ꯊꯤꯖꯤꯟꯕ ꯑꯁꯤꯅꯃꯛ ꯍꯥꯌꯔꯤ ꯃꯗꯨꯗꯤ ꯃꯁꯤꯡ ꯑꯃꯥ ꯁ꯭ꯄꯤꯟ 37 ꯗ ꯑꯃꯨꯛꯇ ꯊꯣꯛꯇꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 3 ꯗꯒꯤ 1 ꯃꯔꯛ ꯂꯩ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯍꯩ ꯕꯣꯔꯗꯇ ꯃꯇꯝ ꯄꯨꯝꯅꯃꯛꯇ “ꯏꯪꯕ” ꯃꯁꯤꯡ ꯈꯔꯥ ꯎꯏ꯫

ꯁ꯭ꯄꯤꯟp(ꯃꯥꯏꯄꯥꯛꯇꯕ, ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ)p(ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯑꯃꯨꯛ ꯃꯥꯏꯄꯥꯛꯄ)
1076.0%24.0%
3736.3%63.7%
7413.2%86.8%
1006.5%93.5%
1501.7%98.3%
2000.4%99.6%
(36/37)ⁿ ꯑꯃꯁꯨꯡ 1 − (36/37)ⁿ꯫ ꯁ꯭ꯄꯤꯟ 100 ꯒꯤ ꯃꯇꯨꯡꯗꯁꯨ ꯃꯁꯤꯡ ꯇꯔꯥꯃꯉꯥ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯥ ꯊꯣꯛꯂꯣꯏ꯫

ꯔꯨꯂꯦꯠꯀꯤ ꯃꯍꯩꯁꯤꯡ: ꯕꯣꯔꯗ ꯄꯥꯕ

ꯉꯥꯏꯒꯗꯕ ꯃꯇꯝ

ꯑꯦꯚꯔꯦꯖꯗ ꯁ꯭ꯇ꯭ꯔꯦꯠ-ꯑꯞ ꯃꯁꯤꯡ ꯑꯃꯥ ꯁ꯭ꯄꯤꯟ 37 ꯈꯨꯗꯤꯡꯗ ꯑꯃꯨꯛ ꯊꯣꯛꯏ, ꯑꯗꯨꯕꯨ ꯉꯥꯏꯕꯒꯤ ꯃꯇꯝ ꯑꯁꯤ ꯌꯥꯝꯅꯥ ꯍꯣꯡꯕ ꯌꯥꯏ: ꯉꯥꯏꯕꯒꯤ ꯃꯤꯗꯤꯌꯥꯟ ꯁ꯭ꯄꯤꯟ 25 ꯃꯔꯛꯅꯤ (ꯃꯇꯃꯒꯤ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕꯗ ꯃꯁꯤꯗꯒꯤ ꯊꯨꯅ ꯂꯥꯛꯏ) ꯑꯃꯁꯨꯡ ꯉꯥꯏꯕ ꯇꯔꯥꯅꯤ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯥ ꯁ꯭ꯄꯤꯟ 110 ꯍꯦꯟꯏ꯫ ꯖꯤꯑꯣꯃꯦꯠꯔꯤꯛ ꯄ꯭ꯔꯣꯁꯦꯁ ꯑꯃꯒꯤ ꯉꯥꯏꯕꯒꯤ ꯃꯇꯃꯁꯤꯡꯒꯤ ꯃꯇꯥꯏ ꯁꯥꯡꯏ, ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ 60 ꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯁꯤꯡ ꯑꯃꯥ ꯂꯥꯛꯀꯗꯕꯅꯤ ꯍꯥꯌꯅ “ꯈꯉꯕ” ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯃꯇꯝ ꯃꯉꯥ ꯈꯨꯗꯤꯡꯗ ꯑꯃꯨꯛ ꯊꯣꯛꯄ ꯋꯥꯐꯝ ꯑꯃꯒꯤ ꯃꯇꯥꯡꯗ ꯉꯥꯡꯂꯤ꯫

ꯑꯔꯥꯟꯕ ꯊꯥꯖꯕ: ꯃꯁꯤꯡꯁꯤꯡ ꯊꯣꯛꯀꯗꯕ ꯃꯇꯝ ꯂꯥꯛꯂꯦ

ꯃꯍꯧꯁꯥꯒꯤ ꯑꯔꯥꯟꯕꯁꯤꯡ

ꯑꯅꯤꯃꯛ ꯊꯣꯛꯕ ꯌꯥꯕ ꯊꯧꯗꯣꯀꯁꯤꯡꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯄꯨꯟꯁꯤꯟꯕ (ꯑꯉꯥꯡꯕ ꯅꯠꯔꯒ ꯕꯤꯖꯣꯔ ꯑꯁꯤ 36/37 ꯅꯠꯇꯦ; 26/37 ꯅꯤ, ꯃꯔꯃꯗꯤ ꯃꯁꯤꯡ ꯇꯔꯥ ꯑꯅꯤꯃꯛ ꯑꯣꯏ)꯫ ꯁ꯭ꯄꯤꯟ ꯑꯃꯈꯛꯇ ꯊꯣꯀꯄ ꯊꯧꯗꯣꯀꯁꯤꯡꯒꯤꯗꯃꯛ ꯃꯔꯥꯡ ꯀꯥꯏꯕ (ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ ꯑꯉꯥꯡꯕ ꯑꯃꯁꯨꯡ ꯕꯤꯖꯣꯔ ꯑꯁꯤ 10/37 ꯅꯤ, 18/37 × 18/37 ꯅꯠꯇꯦ)꯫ ꯍꯥꯟꯅꯒꯤ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯕꯨ ꯍꯧꯖꯤꯛ ꯕꯦꯠ ꯊꯝꯂꯤꯕ ꯃꯊꯪ ꯃꯊꯪꯒꯤ ꯁꯔꯨꯛ ꯑꯃꯥ ꯑꯣꯏꯅ ꯂꯧꯕ: ꯑꯉꯥꯡꯕ ꯇꯔꯥꯒꯤ ꯃꯇꯨꯡꯗ ꯇꯔꯥꯃꯥꯊꯣꯏꯁꯨꯕ ꯑꯉꯥꯡꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 18/37 ꯅꯤ, (18/37)¹¹ ꯅꯠꯇꯦ꯫

ꯔꯨꯂꯦꯠꯇ ꯑꯣꯗꯁ ꯀꯔꯤꯅꯣ, ꯑꯃꯁꯨꯡ ꯃꯈꯣꯌ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯗꯒꯤ ꯀꯔꯝꯅ ꯈꯦꯠꯅꯕꯒꯦ?

ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯅ ꯄꯦꯑꯥꯎꯠꯁꯤꯡꯁꯦꯜꯄꯦꯑꯥꯎꯠꯃꯥꯏꯄꯥꯛꯄ ꯕꯦꯠ ꯑꯃꯅ ꯍꯜꯂꯛꯄ ꯁꯦꯜ, ꯍꯜꯂꯀꯄ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ ꯃꯊꯛꯇ “X ꯗꯒꯤ 1” ꯍꯥꯌꯅ ꯍꯥꯌꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯣꯗꯁ ꯑꯣꯏꯅ ꯍꯥꯌꯏ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ 1/37 ꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯅ ꯃꯥꯏꯄꯥꯛꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯁꯤꯡ ꯑꯃꯗ ꯔꯨꯂꯦꯠꯇ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯑꯣꯗꯁ ꯃꯥꯏꯄꯥꯛꯄꯒꯤ ꯃꯥꯌꯣꯛꯇ 36 ꯗꯒꯤ 1 ꯅꯤ꯫ ꯃꯔꯝ ꯑꯗꯨꯅ 35 ꯗꯒꯤ 1 ꯒꯤ ꯄꯦꯑꯥꯎꯠ ꯑꯁꯤ ꯌꯨꯅꯤꯠꯁꯦꯜꯌꯨꯅꯤꯠꯁꯤꯁ꯭ꯇꯦꯝ ꯅꯠꯔꯒ ꯁꯥꯟꯅꯔꯤꯕ ꯑꯃꯅ ꯁꯤꯖꯤꯟꯅꯕ ꯃꯔꯨꯑꯣꯏꯕ ꯊꯝꯂꯕ ꯁꯦꯜ꯫ ꯄ꯭ꯔꯣꯒ꯭ꯔꯦꯁꯅꯁꯤꯡ ꯌꯨꯅꯤꯠꯇ ꯁꯟꯗꯣꯛꯂꯤ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯈꯣꯌ ꯀꯔꯤꯒꯨꯝꯕ ꯇꯦꯕꯜꯗ ꯆꯠꯂꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯋꯥꯠꯂꯤ, ꯃꯁꯤꯅꯤ ꯃꯍꯧꯁꯥꯒꯤ ꯃꯑꯣꯡꯗ ꯂꯩꯕ ꯍꯥꯎꯁ ꯑꯦꯖꯃꯦꯊꯃꯦꯇꯤꯛꯁꯍꯥꯎꯁ ꯑꯦꯖꯊꯝꯂꯕ ꯁꯦꯜ ꯈꯨꯗꯤꯡꯗꯒꯤ ꯀꯦꯁꯤꯅꯣꯅ ꯑꯦꯚꯔꯦꯖꯗ ꯊꯃꯖꯤꯜꯂꯤꯕ ꯁꯔꯨꯛ: ꯌꯨꯔꯣꯄꯤꯌꯟ ꯔꯨꯂꯦꯠꯇ 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →꯫ ꯍꯣꯡꯗꯣꯛꯄ: ꯃꯥꯌꯣꯛꯇꯒꯤ ꯑꯣꯗꯁ = (1 − p)/p; ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ = 1/(ꯑꯣꯗꯁ + 1)꯫

ꯐꯣꯔꯃꯨꯂꯥ

p(ꯕꯦꯠ) = n / 37
p(A ꯃꯇꯨꯡꯗ B) = p(A) · p(B)
p(k ꯗ ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯑꯃꯨꯛ) = 1 − (1 − p)ᵏ
ꯃꯥꯌꯣꯛꯇꯒꯤ ꯑꯣꯗꯁ = (1 − p) / p

ꯋꯥꯍꯪꯁꯤꯡ

ꯃꯈꯥ ꯆꯠꯅꯅ ꯖꯤꯔꯣ ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥꯅꯣ?

(1/37)² = 1/1369 ≈ 0.073%.

ꯑꯉꯥꯡꯕ ꯅꯠꯔꯒ ꯑꯃꯨꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥꯅꯣ?

36/37 = 97.3%꯫ ꯑꯇꯣꯞꯄ ꯑꯗꯨ ꯖꯤꯔꯣꯅꯤ꯫

17 ꯑꯁꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯌꯥꯝꯅꯥ ꯊꯣꯀꯄ ꯃꯁꯤꯡꯅꯣ?

37 ꯄꯨꯝꯅꯃꯛ 1/37 ꯅꯤ꯫ ꯇꯔꯥꯇꯔꯦꯠ ꯑꯁꯤ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯌꯥꯝꯅꯥ ꯕꯦꯠ ꯊꯝꯕ ꯃꯁꯤꯡꯅꯤ, ꯃꯁꯤ ꯃꯤꯑꯣꯏꯁꯤꯡꯒꯤ ꯃꯇꯥꯡꯗ ꯂꯩꯕ ꯑꯆꯨꯝꯕ ꯑꯃꯅꯤ꯫

ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ

ꯃꯁꯤꯁꯤꯡ ꯑꯍꯥꯅꯕꯗ ꯅꯍꯥꯛ ꯃꯁꯥꯃꯛꯅ ꯍꯣꯠꯅꯕꯤꯌꯨ꯫ ꯄꯥꯎꯈꯨꯝ ꯈꯨꯗꯤꯡꯃꯛ ꯊꯨꯡꯗꯨꯅ ꯊꯝꯂꯤ; ꯁꯦꯝ ꯁꯥꯔꯕ ꯃꯇꯃꯗ ꯍꯥꯡꯗꯣꯛꯄꯤꯌꯨ꯫

  1. ꯅꯍꯥꯛꯅ ꯁ꯭ꯄꯤꯟ ꯈꯨꯗꯤꯡꯗ ꯑꯉꯥꯡꯕꯕꯦꯠꯑꯉꯥꯡꯕꯑꯉꯥꯡꯕ ꯃꯁꯤꯡ 18 ꯗ ꯊꯝꯕ ꯆꯞ ꯃꯥꯟꯅꯕ ꯕꯦꯠ꯫ ꯐ꯭ꯔꯦꯟꯆ: ꯔꯨꯖ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯗ ꯊꯝꯏ꯫ ꯅꯍꯥꯛꯀꯤ ꯃꯉꯥꯁꯨꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯗꯨ ꯆꯨꯝꯅ ꯅꯤꯄꯥꯟꯁꯨꯕ ꯁ꯭ꯄꯤꯟꯗ ꯂꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥ? ꯑꯃꯁꯨꯡ ꯑꯍꯥꯅꯕ ꯁ꯭ꯄꯤꯟ ꯅꯤꯄꯥꯅꯒꯤ ꯃꯅꯨꯡꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯉꯥ ꯐꯪꯕꯒꯤ?

    ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ

    ꯄꯥꯎꯈꯨꯝ ꯃꯉꯥꯁꯨꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯗꯨ ꯁ꯭ꯄꯤꯟ ꯅꯤꯄꯥꯟꯗ ꯂꯥꯛꯄꯒꯤ 12.9%, 8 ꯗ 1 ꯈꯔ꯫ ꯃꯗꯨ ꯐꯥꯑꯣꯕꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯉꯥꯒꯤ 33.4%꯫

    ꯁ꯭ꯄꯤꯟ ꯅꯤꯄꯥꯟꯗ ꯃꯉꯥꯁꯨꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯍꯥꯌꯕꯁꯤ ꯋꯥꯐꯝ ꯑꯅꯤꯅꯤ: ꯁ꯭ꯄꯤꯟ ꯅꯤꯄꯥꯟꯁꯨꯕꯅ ꯃꯥꯏꯄꯥꯀꯏ, ꯑꯃꯁꯨꯡ ꯑꯍꯥꯅꯕ ꯁ꯭ꯄꯤꯟ ꯇꯔꯦꯠꯇ ꯆꯨꯝꯅ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯔꯤ ꯑꯃꯁꯨꯡ ꯃꯥꯏꯊꯤꯕ ꯑꯍꯨꯝ ꯂꯩ, ꯀꯔꯤꯒꯨꯝꯕ ꯃꯊꯪ ꯃꯊꯪꯗ꯫ ꯁ꯭ꯄꯤꯟ ꯇꯔꯦꯠꯀꯤ ꯃꯅꯨꯡꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯔꯤ ꯊꯝꯅꯕ ꯃꯑꯣꯡ 35 ꯂꯩ꯫

    ꯃꯔꯝ ꯑꯗꯨꯅ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ 35 × (18/37)⁵ × (19/37)³ = 35 × 0.02725 × 0.1354 = 12.9%꯫

    ꯁ꯭ꯄꯤꯟ ꯅꯤꯄꯥꯟ ꯐꯥꯑꯣꯕꯗ ꯃꯥꯏꯄꯥꯛꯄ ꯃꯉꯥꯒꯤꯗꯃꯛ, ꯃꯉꯥꯁꯨꯕ ꯃꯥꯏꯄꯥꯛꯄ ꯑꯗꯨ ꯁ꯭ꯄꯤꯟ ꯃꯉꯥ, ꯇꯔꯨꯛ ꯑꯃꯁꯨꯡ ꯇꯔꯦꯠꯇ ꯂꯥꯛꯄꯒꯤ ꯃꯈꯜ ꯑꯗꯨꯃꯛꯀꯤ ꯇꯔꯝ ꯍꯥꯄꯆꯤꯜꯂꯨ: 2.7% + 7.0% + 10.8% + 12.9% = 33.4%꯫ ꯁ꯭ꯇꯦꯇꯤꯁ꯭ꯇꯤꯛꯁ ꯇꯧꯔꯤꯕꯁꯤꯡꯅ ꯃꯁꯤꯕꯨ ꯅꯦꯒꯦꯇꯤꯕ ꯕꯥꯏꯅꯣꯃꯤꯌꯦꯜ ꯗꯤꯁ꯭ꯇ꯭ꯔꯤꯕ꯭ꯌꯨꯁꯟ ꯍꯥꯌꯅ ꯀꯧꯏ: ꯃꯥꯌ ꯄꯥꯀꯄ ꯃꯁꯤꯡ ꯑꯃꯒꯤꯗꯃꯛ ꯍꯣꯠꯅꯕ ꯀꯌꯥ ꯆꯪꯒꯅꯤ꯫ Taylor (2021) ꯅ ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔ ꯑꯃꯗ ꯋꯥꯍꯪ ꯑꯗꯨꯃꯛ ꯍꯤꯁꯥꯕ ꯇꯧꯔꯤ, 12.2%꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯄꯣꯀꯦꯠꯁꯤꯡ ꯊꯤꯕꯤꯌꯨ꯫ 37 ꯅ ꯌꯦꯟꯊꯣꯀꯄꯤꯌꯨ꯫ ꯃꯊꯪ ꯃꯊꯪꯒꯤꯗꯃꯛ ꯃꯔꯥꯡ ꯀꯥꯏꯕꯤꯌꯨ꯫ ꯂꯣꯏꯔꯦ꯫

ꯄꯣꯀꯦꯠꯁꯤꯡ ꯊꯤꯕꯤꯌꯨ꯫ 37 ꯅ ꯌꯦꯟꯊꯣꯀꯄꯤꯌꯨ꯫ ꯃꯊꯪ ꯃꯊꯪꯒꯤꯗꯃꯛ ꯃꯔꯥꯡ ꯀꯥꯏꯕꯤꯌꯨ꯫ ꯂꯣꯏꯔꯦ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

  1. Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, 3 ꯁꯨꯕ ꯑꯦꯗꯤꯁꯟ, 1968꯫ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕ (gambler’s ruin), ꯆꯦꯞꯇꯔ XIV꯫
  2. Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling. Springer, 2010꯫ ꯆꯦꯞꯇꯔ 13, ꯔꯨꯂꯦꯠ꯫
  3. Taylor, D. G. Games, Gambling, and Probability: An Introduction to Mathematics, 2nd ed. CRC Press, 2021꯫
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