ꯔꯨꯂꯦꯠꯀꯤ ꯃꯦꯊꯃꯦꯇꯤꯛꯁ · ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯤ ꯁꯃꯁ꯭ꯌꯥ · ꯃꯤꯅꯤꯠ 7

ꯁꯃꯁ꯭ꯌꯥ: ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯆꯛꯔ

ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯅꯕ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ? ꯃꯤ ꯀꯌꯥꯅ ꯈꯟꯖꯤꯟꯂꯤꯕꯗꯒꯤ ꯌꯥꯝꯅꯥ ꯍꯟꯅ꯫

ꯊꯨꯅ ꯄꯥꯎꯈꯨꯝ

ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → 37 ꯂꯩꯕ ꯆꯛꯔ ꯑꯃꯗ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯁꯃꯁ꯭ꯌꯥ: ꯁ꯭ꯄꯤꯟ 8 ꯈꯛꯇꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯣꯀꯈ꯭ꯔꯦ ꯍꯥꯌꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ ꯇꯉꯥꯏꯗꯒꯤ ꯍꯦꯟꯏ꯫ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄꯁꯤꯡ ꯑꯁꯤ ꯄꯦꯇꯔꯟ ꯑꯣꯏꯅ ꯂꯧꯏ; ꯃꯈꯣꯌ ꯑꯁꯤ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯒꯤ ꯊꯥꯖꯒꯗꯕ ꯃꯑꯣꯡꯅꯤ꯫

ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄꯒꯤ 50% ꯈꯨꯗꯣꯡꯆꯥꯕ

ꯁ꯭ꯄꯤꯟ 8

90% ꯈꯨꯗꯣꯡꯆꯥꯕ

ꯁ꯭ꯄꯤꯟ 14

99% ꯈꯨꯗꯣꯡꯆꯥꯕ

ꯁ꯭ꯄꯤꯟ 20

ꯑꯍꯥꯅꯕ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯐꯥꯑꯣꯕꯒꯤ ꯐꯪꯒꯗꯕ ꯁ꯭ꯄꯤꯟ

≈ 8.3

ꯁꯃꯁ꯭ꯌꯥ

ꯆꯨꯝꯃꯤꯟꯅꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔ ꯑꯃꯥ ꯀꯣꯏꯍꯟꯕꯤꯌꯨ꯫ ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯁ꯭ꯄꯤꯟ ꯑꯅꯤꯅ ꯃꯁꯤꯡ ꯑꯗꯨꯃꯛ ꯎꯠꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯁꯤ ꯇꯉꯥꯏꯗꯒꯤ ꯍꯦꯅꯅꯕ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ? ꯁꯥꯟꯅꯔꯤꯕ ꯀꯌꯥꯅ 37 ꯒꯤ ꯇꯉꯥꯏ, 18 ꯅꯠꯔꯒ 19 ꯃꯔꯥꯡ ꯀꯥꯏ ꯍꯥꯌꯅ ꯈꯟꯖꯤꯟꯂꯤ꯫ ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨꯗꯤ 8 ꯅꯤ꯫

ꯁꯣꯜꯌꯨꯁꯟ

ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯇꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯊꯤꯖꯤꯟꯗꯨꯅ ꯑꯃꯗꯒꯤ ꯂꯧꯊꯣꯀꯎ꯫ ꯁ꯭ꯄꯤꯟ k ꯒꯤ ꯃꯇꯨꯡꯗ, p(ꯄꯨꯝꯅꯃꯛ ꯈꯦꯠꯅꯕ) = (37/37)(36/37)(35/37)…((38 − k)/37)꯫ k = 8 ꯒꯤꯗꯃꯛ: 1 × 0.973 × 0.946 × 0.919 × 0.892 × 0.865 × 0.838 × 0.811 ≈ 0.44, ꯃꯔꯝ ꯑꯗꯨꯅ p(ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ) ≈ 0.56꯫ k = 14 ꯒꯤꯗꯃꯛ ꯃꯁꯤ 0.93; k = 20 ꯒꯤꯗꯃꯛ ꯃꯁꯤ 0.996꯫ ꯈꯜꯂꯕ ꯑꯗꯨ ꯑꯔꯥꯟꯕꯒꯤ ꯃꯔꯝ ꯑꯗꯨꯗꯤ ꯁ꯭ꯄꯤꯟꯒꯤ ꯄꯦꯌꯔꯁꯤꯡꯒꯤ ꯃꯁꯤꯡ ꯑꯁꯤ k² ꯒꯨꯝꯅ ꯍꯦꯅꯒꯠꯂꯛꯏ, ꯑꯃꯁꯨꯡ ꯀꯔꯤꯒꯨꯝꯕ ꯄꯦꯌꯔ ꯑꯃꯃꯛ ꯆꯥꯟꯅꯕ ꯌꯥꯏ꯫

ꯁ꯭ꯄꯤꯟ kp(ꯄꯨꯝꯅꯃꯛ ꯈꯦꯠꯅꯕ)p(ꯌꯥꯃꯗ꯭ꯔꯕꯗ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯑꯃꯥ)

575.7%24.3%

843.8%56.2%

1026.4%73.6%

147.1%92.9%

200.4%99.6%

37≈ 0%≈ 100%

p(ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯇꯕ) = 37! / ((37 − k)! · 37ᵏ)꯫

ꯇꯦꯕꯜꯗ ꯃꯁꯤ ꯀꯔꯤꯒꯤ ꯃꯔꯨ ꯑꯣꯏꯕꯒꯦ

ꯑꯔꯣꯏꯕ ꯃꯁꯤꯡ 20 ꯎꯠꯂꯤꯕ ꯃꯍꯩ ꯕꯣꯔꯗ ꯑꯃꯅ ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯃꯔꯥꯡ ꯀꯥꯏꯅ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯑꯃꯥ ꯎꯠꯀꯅꯤ, ꯌꯥꯝꯅꯥ ꯀꯌꯥꯗ ꯑꯅꯤ ꯅꯠꯔꯒ ꯑꯍꯨꯝ꯫ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ “ꯁ꯭ꯄꯤꯟ ꯇꯔꯥꯗ 17 ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯣꯀꯈꯤ” ꯍꯥꯌꯕ ꯎꯏ ꯑꯃꯁꯨꯡ 17 ꯁꯥꯠꯄ ꯃꯁꯤꯡꯅꯤ ꯍꯥꯌꯅ ꯂꯧꯏ; ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯃꯁꯤꯡ ꯊꯤꯕꯅ ꯍꯥꯌꯔꯤ ꯃꯗꯨꯗꯤ ꯁ꯭ꯄꯤꯟ ꯇꯔꯥꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯑꯁꯤ ꯃꯇꯃꯒꯤ 74% ꯗ ꯊꯣꯛꯏ ꯑꯃꯁꯨꯡ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯀꯄ ꯃꯁꯤꯡ ꯑꯗꯨ ꯔꯦꯟꯗꯝꯅꯤ꯫ ꯄꯦꯇꯔꯟ ꯑꯗꯨ ꯑꯁꯦꯡꯕꯅꯤ; ꯃꯗꯨꯒꯤ ꯑꯔꯊ ꯑꯗꯨꯗꯤ ꯑꯁꯦꯡꯕ ꯅꯠꯇꯦ꯫

ꯁ꯭ꯄꯤꯟ k ꯒꯤ ꯃꯇꯨꯡꯗ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯀꯈꯤꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ%

ꯁ꯭ꯄꯤꯟ 4

16%

ꯁ꯭ꯄꯤꯟ 6

36%

ꯁ꯭ꯄꯤꯟ 8

56%

ꯁ꯭ꯄꯤꯟ 10

74%

ꯁ꯭ꯄꯤꯟ 14

93%

ꯁ꯭ꯄꯤꯟ 20

99.6%

049.8099.6%

ꯔꯨꯂꯦꯠꯀꯤ ꯃꯍꯩꯁꯤꯡ: ꯕꯣꯔꯗ ꯄꯥꯕ

ꯃꯇꯨꯡꯒꯤ ꯁꯃꯁ꯭ꯌꯥ

ꯑꯈꯟꯅꯕ ꯃꯁꯤꯡ ꯑꯃꯥ, ꯈꯨꯗꯝꯅ 17, ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯣꯛꯅꯕ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ? ꯃꯁꯤ ꯈꯦꯠꯅꯕ ꯋꯥꯍꯪ ꯑꯃꯅꯤ ꯑꯃꯁꯨꯡ ꯃꯁꯤꯒꯤ ꯄꯥꯎꯈꯨꯝ ꯌꯥꯝꯅꯥ ꯆꯥꯎꯏ: ꯉꯥꯏꯒꯗꯕ ꯃꯇꯝ ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ 74, ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ 20 ꯒꯤ ꯃꯅꯨꯡꯗ 17 ꯑꯅꯤ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯁꯤ 10% ꯃꯔꯥꯡ ꯀꯥꯏ꯫ “ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯀꯏ” (ꯁ꯭ꯄꯤꯟ 8) ꯑꯃꯁꯨꯡ “ꯃꯁꯤꯡ ꯑꯁꯤ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯀꯏ” (ꯁ꯭ꯄꯤꯟ 74) ꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯕ ꯈꯦꯠꯅꯕ ꯑꯁꯤ ꯃꯇꯨꯡꯗ ꯅꯍꯥꯛꯅ ꯎꯕ ꯐꯪꯕ ꯄꯦꯇꯔꯟ ꯑꯃꯁꯨꯡ ꯃꯃꯥꯡꯗ ꯅꯍꯥꯛꯅ ꯇꯧꯕ ꯄꯥꯎꯖꯦꯜ ꯑꯃꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯕ ꯈꯦꯠꯅꯕ ꯄꯨꯝꯅꯃꯛꯅꯤ꯫

ꯇꯧꯔꯒ ꯌꯦꯡꯕꯤꯌꯨ

ꯗꯦꯃꯣ ꯒꯦꯝ ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ ꯇꯔꯥ ꯆꯂꯥꯏꯗꯨꯅ ꯍꯤꯁ꯭ꯇꯔꯤ ꯑꯗꯨ ꯌꯦꯡꯕꯤꯌꯨ꯫ ꯌꯥꯝꯅꯥ ꯀꯌꯥꯗ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯑꯃꯥ ꯂꯩꯒꯅꯤ꯫ ꯑꯃꯨꯛ ꯍꯟꯅ ꯆꯂꯥꯏꯕꯤꯌꯨ꯫ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯃꯁꯤꯡ ꯑꯗꯨ ꯈꯦꯠꯅꯒꯅꯤ꯫ ꯃꯁꯤ ꯑꯃꯨꯛ ꯇꯔꯥ ꯇꯧꯔꯕꯗꯤ ꯅꯍꯥꯛꯅ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯁꯃꯁ꯭ꯌꯥꯃꯦꯊꯃꯦꯇꯤꯛꯁꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯁꯃꯁ꯭ꯌꯥꯃꯤ ꯑꯅꯤꯒꯤ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠ ꯃꯥꯟꯅꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯌꯥꯝꯅꯕꯥ ꯃꯤ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ, ꯅꯠꯔꯒ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯣꯛꯅꯕꯥ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ꯫ ꯄꯣꯀꯦꯠ 37 ꯂꯩꯕ ꯆꯛꯔꯗ ꯁ꯭ꯄꯤꯟ 8 ꯅ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕꯗꯒꯤ ꯍꯦꯟꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯄꯤꯕꯗ ꯃꯇꯤꯛ ꯆꯥꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯎꯔꯦ; ꯑꯃꯨꯛ ꯂꯤꯁꯤꯡ ꯑꯃꯥ ꯇꯧꯔꯕꯗꯤ (ꯁꯤꯃꯨꯂꯦꯇꯔꯁꯤꯡꯅ ꯇꯧꯕ ꯉꯝꯃꯤ) ꯅꯍꯥꯛꯅ ꯃꯗꯨ ꯆꯥꯡ ꯊꯤꯔꯦ꯫

ꯐꯣꯔꯃꯨꯂꯥ

p(k ꯗ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯇꯕ) = Π (38 − i)/37, i = 1…k ꯒꯤꯗꯃꯛ

p(ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ) = 1 − p(ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯇꯕ)

ꯋꯥꯍꯪꯁꯤꯡ

ꯃꯁꯤ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯄꯦꯔꯥꯗꯣꯛꯁꯀꯥ ꯑꯗꯨꯃꯛꯇꯔꯥ?

ꯆꯞ ꯃꯥꯟꯅꯕꯅꯤ, ꯅꯨꯃꯤꯠ 365 ꯒꯤ ꯃꯍꯨꯠꯇ ꯄꯣꯀꯦꯠ 37 ꯂꯩꯕꯗ꯫ ꯃꯤ 23 ꯅ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤꯗꯃꯛ 50% ꯄꯤ; ꯁ꯭ꯄꯤꯟ 8 ꯅ ꯆꯛꯔꯒꯤꯗꯃꯛ 56% ꯄꯤ꯫

ꯃꯁꯤꯡ ꯑꯗꯨꯃꯛ ꯑꯃꯨꯛ ꯑꯍꯨꯝ ꯊꯣꯛꯄꯗꯤ ꯀꯔꯝꯅꯣ?

ꯁ꯭ꯄꯤꯟ 19 ꯃꯔꯥꯡ ꯀꯥꯏꯒꯤ ꯃꯇꯨꯡꯗ 50%꯫ ꯃꯁꯤꯁꯨ ꯃꯤꯅꯝ ꯊꯧꯗꯣꯛꯅꯤ꯫

ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯑꯃꯅ ꯕꯥꯏꯌꯥꯁ ꯇꯥꯀꯄꯔꯥ?

ꯅꯠꯇꯦ꯫ ꯆꯛꯔ ꯑꯃꯗꯒꯤ ꯁ꯭ꯄꯤꯟ ꯂꯤꯁꯤꯡ ꯀꯌꯥꯅ ꯇꯥꯀꯄ ꯌꯥꯏ; ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯛꯄ ꯑꯃꯈꯛꯇꯅ ꯀꯩꯗꯧꯉꯩꯗꯁꯨ ꯇꯥꯀꯄ ꯉꯃꯗꯦ꯫

ꯃꯦꯊꯃꯦꯇꯤꯛꯁꯀꯥ ꯁꯥꯟꯅꯕ

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

ꯑꯃꯦꯔꯤꯀꯟ ꯆꯛꯔ ꯑꯃꯒꯤ ꯃꯅꯥꯛꯇ ꯂꯩꯕ ꯃꯍꯩ ꯕꯣꯔꯗ ꯑꯃꯅ ꯑꯔꯣꯏꯕ ꯁ꯭ꯄꯤꯟ 16 ꯎꯠꯂꯤ꯫ ꯃꯗꯨꯗ ꯃꯁꯤꯡ ꯑꯃꯠꯇꯥ ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯣꯛꯇꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥꯅꯣ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ ꯈꯟꯊꯕꯗ 2.5%: ꯕꯣꯔꯗ 40 ꯗ ꯈꯟꯊꯕꯗ 39 ꯅ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕꯗ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯣꯀꯄ ꯑꯃꯥ ꯎꯠꯂꯤ꯫
ꯁ꯭ꯄꯤꯟ ꯑꯃꯃꯃꯒꯤ ꯃꯇꯨꯡ ꯏꯟꯅ ꯆꯠꯂꯁꯤ꯫ ꯑꯍꯥꯅꯕ ꯁ꯭ꯄꯤꯟ ꯑꯗꯨ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯑꯣꯏꯕ ꯌꯥꯏ꯫ ꯑꯅꯤꯁꯨꯕꯥ ꯑꯗꯨꯅ ꯃꯗꯨ ꯂꯥꯛꯂꯣꯏꯗꯕꯅꯤ: 38 ꯗ 37꯫ ꯑꯍꯨꯃꯁꯨꯕꯥ ꯑꯗꯨꯅ ꯑꯅꯤꯃꯛ ꯂꯥꯛꯂꯣꯏꯗꯕꯅꯤ: 38 ꯗ 36꯫ ꯇꯔꯥꯅꯤꯇꯔꯨꯛꯁꯨꯕꯥ ꯑꯗꯨꯅ ꯃꯁꯤꯡ ꯇꯔꯥꯃꯉꯥ ꯂꯥꯛꯂꯣꯏꯗꯕꯅꯤ: 38 ꯗ 23꯫
ꯃꯥꯏꯄꯨꯟꯕꯤꯌꯨ: 38/38 × 37/38 × 36/38 × … × 23/38 ≈ 0.0246꯫
ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯣꯀꯄ ꯂꯩꯇꯕ ꯕꯣꯔꯗ ꯑꯗꯨꯅꯤ ꯈꯟꯗꯕ꯫ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯣꯀꯄ ꯂꯩꯕ ꯕꯣꯔꯗ ꯑꯃꯅ ꯆꯛꯔ ꯑꯗꯨꯒꯤ ꯃꯔꯃꯗ ꯀꯔꯤꯁꯨ ꯍꯥꯌꯗꯦ꯫
ꯌꯨꯔꯣꯄꯤꯌꯟ ꯆꯛꯔ ꯑꯃꯒꯤ ꯁ꯭ꯄꯤꯟ ꯇꯔꯥꯗ, 17 ꯑꯁꯤ ꯑꯃꯨꯛ ꯃꯉꯥ ꯈꯛꯇ ꯊꯣꯀꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯀꯌꯥꯅꯣ? ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ, ꯀꯅꯥꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ, ꯑꯃꯨꯛ ꯃꯉꯥ ꯅꯠꯔꯒ ꯍꯦꯟꯅꯥ ꯊꯣꯀꯄꯒꯤ? ꯑꯃꯁꯨꯡ ꯁ꯭ꯄꯤꯟ ꯃꯔꯤꯗ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ ꯈ꯭ꯕꯥꯏꯗꯒꯤ ꯅꯦꯝꯕꯗ ꯑꯃꯨꯛ ꯑꯍꯨꯝ ꯊꯣꯀꯄꯒꯤ?
ꯄꯥꯎꯈꯨꯝ ꯎꯠꯄ
ꯄꯥꯎꯈꯨꯝ 17 ꯑꯃꯨꯛ ꯃꯉꯥ ꯈꯛꯇ: 315,576 ꯗ 1꯫ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯃꯉꯥ ꯅꯠꯔꯒ ꯍꯦꯟꯅꯥ: ꯈꯟꯊꯕꯗ 8,333 ꯗ 1꯫ ꯁ꯭ꯄꯤꯟ ꯃꯔꯤꯗ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯑꯍꯨꯝ ꯅꯠꯔꯒ ꯍꯦꯟꯅꯥ: 349 ꯗ 1꯫
17 ꯑꯃꯨꯛ ꯃꯉꯥ: ꯁ꯭ꯄꯤꯟ ꯇꯔꯥꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ ꯀꯅꯥꯒꯤ ꯃꯉꯥꯅꯣ ꯈꯅꯕꯤꯌꯨ, ꯂꯝꯕꯤ 252, ꯈꯨꯗꯤꯡꯃꯛꯀꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ (1/37)⁵ × (36/37)⁵꯫ ꯄꯨꯟꯅ, 315,576 ꯗ 1꯫
ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ: ꯃꯁꯤꯡ 37 ꯒꯤ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯑꯃꯨꯛ ꯃꯉꯥ ꯅꯠꯔꯒ ꯍꯦꯟꯅꯥ ꯂꯥꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ 308,325 ꯗ 1 ꯂꯩ, ꯃꯁꯤꯅ 308,325 ꯗ 37, ꯅꯠꯔꯒ 8,333 ꯗ 1 ꯄꯤ꯫ ꯃꯁꯤꯡ ꯑꯅꯤꯃꯛꯅ ꯑꯃꯨꯛ ꯃꯉꯥ ꯃꯉꯥ ꯂꯥꯛꯄꯒꯤ ꯈꯟꯗꯕ ꯐꯤꯚꯝ ꯑꯗꯨ ꯑꯃꯨꯛ ꯑꯅꯤ ꯊꯤꯔꯦ, ꯑꯗꯨꯕꯨ ꯃꯗꯨ ꯂꯧꯊꯣꯛꯂꯕꯁꯨ ꯆꯨꯃꯊꯣꯀꯄꯒꯤ ꯊꯥꯛ ꯑꯁꯤꯗ ꯀꯔꯤꯁꯨ ꯍꯣꯡꯗꯣꯀꯄꯗꯦ꯫
ꯁ꯭ꯄꯤꯟ ꯃꯔꯤꯗ ꯑꯃꯨꯛ ꯑꯍꯨꯝ: ꯃꯁꯤꯡ ꯑꯃꯒꯤꯗꯃꯛ, ꯐꯪꯕ ꯌꯥꯕ ꯃꯍꯩ 37⁴ ꯒꯤ ꯃꯅꯨꯡꯗꯒꯤ 4 × 36 + 1 = 145; ꯃꯁꯤꯡ 37 ꯒꯤ ꯀꯅꯥꯒꯨꯝꯕ ꯑꯃꯒꯤꯗꯃꯛ, 145/37³ = 349 ꯗ 1꯫
ꯗꯕꯜ ꯖꯤꯔꯣꯆꯛꯔꯖꯤꯔꯣꯆꯞ ꯃꯥꯟꯅꯕ, ꯗꯖꯟ ꯅꯠꯔꯒ ꯀꯂꯝ ꯕꯦꯠ ꯑꯃꯠꯇꯅ ꯀꯨꯞꯇꯕ ꯑꯁꯪꯕ ꯄꯣꯀꯦꯠ ꯑꯃꯈꯛꯇ; ꯍꯥꯎꯁ ꯑꯦꯖꯀꯤ ꯍꯧꯔꯀꯐꯝꯅꯤ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣ, 0꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯆꯛꯔ ꯑꯃꯒꯤꯗꯃꯛ ꯃꯁꯤꯡꯁꯤꯡ ꯑꯗꯨ 359,275 ꯗ 1, 9,243 ꯗ 1 ꯑꯃꯁꯨꯡ 368 ꯗ 1 ꯅꯤ꯫ “17” ꯑꯃꯁꯨꯡ “ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯥ” ꯒꯤ ꯃꯔꯛꯇ ꯂꯩꯕ ꯈꯦꯠꯅꯕ ꯑꯁꯤ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯁꯃꯁ꯭ꯌꯥꯃꯦꯊꯃꯦꯇꯤꯛꯁꯄꯣꯛꯄ ꯅꯨꯃꯤꯠꯀꯤ ꯁꯃꯁ꯭ꯌꯥꯃꯤ ꯑꯅꯤꯒꯤ ꯄꯣꯛꯄ ꯅꯨꯃꯤꯠ ꯃꯥꯟꯅꯕꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯌꯥꯝꯅꯕꯥ ꯃꯤ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ, ꯅꯠꯔꯒ ꯃꯁꯤꯡ ꯑꯃꯥ ꯑꯃꯨꯛ ꯍꯟꯅꯥ ꯊꯣꯛꯅꯕꯥ ꯁ꯭ꯄꯤꯟ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯕꯒꯦ꯫ ꯄꯣꯀꯦꯠ 37 ꯂꯩꯕ ꯆꯛꯔꯗ ꯁ꯭ꯄꯤꯟ 8 ꯅ ꯁꯔꯨꯛ ꯑꯍꯦꯟꯕꯗꯒꯤ ꯍꯦꯟꯕ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯄꯤꯕꯗ ꯃꯇꯤꯛ ꯆꯥꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨꯅꯤ ꯑꯃꯨꯛ ꯍꯟꯅꯥ: ꯑꯉꯀꯄꯒꯤ ꯂꯝꯕꯤ 37 ꯂꯩ꯫

ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

$ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯊꯨꯅ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯀꯏ꯫ ꯃꯗꯨ ꯀꯔꯤꯅꯣ ꯍꯥꯌꯕꯗꯤ ꯔꯦꯟꯗꯝꯅꯤ꯫$

ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯥ ꯊꯨꯅ ꯑꯃꯨꯛ ꯍꯟꯅ ꯊꯣꯀꯏ꯫ ꯃꯗꯨ ꯀꯔꯤꯅꯣ ꯍꯥꯌꯕꯗꯤ ꯔꯦꯟꯗꯝꯅꯤ꯫

ꯍꯧꯔꯛꯐꯃꯁꯤꯡ

Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1. Wiley, ꯑꯦꯗꯤꯁꯟ 3, 1968꯫ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯃꯥꯡꯍꯟ ꯇꯥꯀꯍꯟꯕ, ꯆꯦꯞꯇꯔ XIV꯫
Wizard of Odds. “Ask the Wizard”, ꯔꯨꯂꯦꯠꯀꯤ ꯋꯥꯍꯪꯁꯤꯡ꯫ ꯑꯒꯁ꯭ꯠ 3, 2026 ꯗ ꯑꯅꯧꯕ ꯑꯣꯏꯍꯅꯈꯤ꯫

ꯌꯦꯡꯁꯤꯅꯈꯤꯕ 2026-09-28ꯃꯣꯗꯦꯜ: ꯌꯨꯔꯣꯄꯤꯌꯟ, ꯁꯤꯡꯒꯜ ꯖꯤꯔꯣꯃꯦꯊꯗꯣꯂꯣꯖꯤ ↗ꯍꯧꯔꯛꯐꯃꯁꯤꯡ ↗