ꯑꯔꯥꯟꯕ ꯊꯥꯖꯕ: ꯃꯁꯤꯡꯁꯤꯡ ꯊꯣꯛꯀꯗꯕ ꯃꯇꯝ ꯂꯥꯛꯂꯦ
“ꯇꯔꯥꯇꯔꯦꯠ ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ 150 ꯗ ꯊꯣꯛꯂꯃꯗꯦ꯫ ꯃꯁꯤ ꯊꯣꯛꯀꯗꯕ ꯃꯇꯝ ꯂꯥꯛꯂꯦ꯫” ꯂꯥꯛꯂꯃꯗꯦ꯫

ꯃꯇꯝ ꯁꯥꯡꯅ ꯊꯣꯛꯂꯃꯗꯕ ꯃꯁꯤꯡ ꯑꯃꯥ ꯃꯊꯪꯒꯤ ꯁ꯭ꯄꯤꯟꯗ ꯑꯇꯣꯞꯄ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯒꯨꯝꯅ ꯆꯨꯃꯅ ꯊꯣꯛꯄ ꯌꯥꯏ: 1/37꯫ ꯃꯁꯤ “ꯊꯣꯛꯀꯗꯕ ꯃꯇꯝ ꯂꯥꯛꯂꯦ” ꯍꯥꯌꯕ ꯊꯥꯖꯕ ꯑꯁꯤ ꯃꯍꯩ ꯕꯣꯔꯗ ꯑꯃꯒ ꯂꯣꯌꯅꯕ ꯖꯨꯌꯥ ꯁꯥꯟꯅꯔꯤꯕꯒꯤ ꯑꯔꯥꯟꯕ ꯋꯥꯈꯜꯅꯤ꯫
ꯍꯥꯌꯔꯤꯕ ꯋꯥ
ꯀꯦꯁꯤꯅꯣꯁꯤꯡꯅ ꯑꯔꯣꯏꯕ ꯃꯍꯩ 20 ꯗꯒꯤ 500 ꯐꯥꯑꯣꯕ ꯎꯠꯂꯤ ꯑꯃꯁꯨꯡ ꯃꯇꯝ ꯈꯔꯒꯤ ꯃꯅꯨꯡꯗ ꯊꯣꯛꯇꯕ “ꯏꯪꯕ” ꯃꯁꯤꯡꯁꯤꯡ ꯃꯇꯝ ꯌꯥꯝꯗ ꯈꯦꯟꯅꯍꯜꯂꯤ꯫ ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯕꯣꯔꯗ ꯑꯗꯨ ꯄꯥꯏ, 17 ꯑꯁꯤ ꯁ꯭ꯄꯤꯟ 150 ꯊꯣꯛꯂꯃꯗꯦ ꯍꯥꯌꯕ ꯎꯏ, ꯑꯃꯁꯨꯡ ꯊꯣꯛꯀꯗꯕ ꯃꯇꯝ ꯂꯥꯛꯂꯦ ꯍꯥꯌꯗꯨꯅ ꯕꯦꯠ ꯊꯝꯃꯤ꯫ ꯋꯥꯈꯜ ꯑꯗꯨꯗꯤ ꯃꯇꯝ ꯁꯥꯡꯅ ꯃꯁꯤꯡ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯇꯃꯒꯤ 1/37 ꯗ ꯊꯣꯀꯏ, ꯃꯔꯝ ꯑꯗꯨꯅ ꯃꯇꯨꯡꯗ ꯂꯦꯃꯍꯧꯔꯕ ꯃꯁꯤꯡ ꯑꯃꯅ ꯃꯈꯨꯠ ꯐꯪꯒꯗꯕꯅꯤ ꯍꯥꯌꯕꯅꯤ꯫
ꯀꯔꯤꯒꯤ ꯑꯔꯥꯟꯕꯅꯣ
ꯁ꯭ꯄꯤꯟꯁꯤꯡ ꯃꯔꯤ ꯂꯩꯅꯗꯦ꯫ ꯕꯣꯜꯈꯨꯠꯂꯥꯏꯕꯣꯜꯔꯣꯇꯔꯒꯤ ꯃꯥꯌꯣꯛꯇ ꯇ꯭ꯔꯦꯛꯇ ꯊꯥꯗꯣꯛꯄ ꯑꯄꯤꯛꯄ ꯕꯣꯜ꯫ ꯍꯧꯖꯤꯛꯀꯤ ꯕꯣꯜꯁꯤꯡ ꯑꯥꯏꯚꯣꯔꯤꯟ ꯅꯠꯔꯒ ꯇꯦꯐ꯭ꯂꯣꯅꯅ ꯁꯦꯝꯃꯤ, 18–21 mm꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨꯅ 17 ꯊꯣꯛꯂꯃꯗꯦ ꯍꯥꯌꯕ ꯈꯉꯗꯦ, ꯑꯃꯁꯨꯡ ꯄꯣꯀꯦꯠꯈꯨꯠꯂꯥꯏꯄꯣꯀꯦꯠꯔꯣꯇꯔꯗ ꯂꯩꯕ ꯃꯁꯤꯡ ꯏꯔꯕ ꯀꯣꯠ 37 ꯒꯤ ꯃꯅꯨꯡꯗ ꯑꯃꯥ꯫ ꯑꯇꯣꯞꯄ ꯃꯃꯤꯡ: ꯁ꯭ꯂꯣꯠ, ꯀꯞ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯗꯨ ꯃꯃꯥꯡꯒꯨꯝꯅ ꯆꯥꯡ ꯃꯥꯟꯅꯩ꯫ ꯃꯇꯝ ꯁꯥꯡꯅ ꯆꯥꯡ ꯑꯗꯨ ꯁꯦꯃꯗꯣꯛꯄꯅꯥ ꯅꯠꯇꯅ ꯃꯁꯤꯡ ꯌꯥꯝꯂꯛꯄꯅꯥ ꯅꯛꯂꯀꯏ: ꯁ꯭ꯄꯤꯟ 10,000 ꯍꯦꯟꯅꯥ ꯆꯠꯂꯕꯥ ꯃꯇꯨꯡꯗ ꯁ꯭ꯄꯤꯟ 150 ꯒꯤ ꯂꯦꯃꯍꯧꯕ ꯑꯁꯤ ꯔꯥꯎꯟꯗ ꯇꯧꯕꯒꯤ ꯑꯁꯣꯏꯕ ꯈꯔꯈꯛ ꯑꯣꯏꯔꯤ, 17 ꯍꯦꯟꯅꯥ ꯌꯥꯝꯅ ꯊꯣꯀꯈꯤꯕꯅꯥ ꯅꯠꯇꯅ ꯁꯦꯝꯄꯜ ꯑꯗꯨ ꯆꯥꯎꯈꯠꯂꯀꯄꯅꯥ꯫ ꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝꯃꯦꯊꯃꯦꯇꯤꯛꯁꯑꯆꯧꯕ ꯃꯁꯤꯡꯒꯤ ꯅꯤꯌꯝꯍꯣꯠꯅꯕꯒꯤ ꯃꯁꯤꯡ ꯍꯦꯅꯒꯠꯂꯀꯄꯒ ꯂꯣꯌꯅꯅ ꯃꯔꯤ ꯂꯩꯅꯗꯕ ꯃꯍꯩꯁꯤꯡꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯑꯗꯨ ꯐꯪꯒꯗꯕ ꯃꯃꯂꯗ ꯅꯛꯂꯛꯏ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯅ ꯃꯁꯤꯡ ꯑꯃꯠꯇꯕꯨ ꯃꯈꯨꯠ ꯐꯪꯅꯕ ꯍꯥꯌꯗꯦ; ꯃꯃꯥꯡꯒꯤ ꯍꯣꯡꯂꯛꯄꯁꯤꯡ ꯄꯨꯝꯅꯃꯛꯀꯥ ꯆꯥꯡꯗꯝꯅꯕꯗ ꯑꯄꯤꯛꯅ ꯑꯣꯏꯔꯛꯀꯗꯕꯅꯤ ꯍꯥꯌꯕꯈꯛꯅꯤ꯫
ꯀꯔꯤꯒꯤ ꯆꯨꯝꯕꯒꯨꯝ ꯐꯥꯑꯣꯕꯒꯦ
ꯃꯔꯃꯗꯤ ꯄꯨꯟꯁꯤꯒꯤ ꯑꯇꯣꯞꯄ ꯁꯔꯨꯛ ꯈꯨꯗꯤꯡꯃꯛꯇ ꯂꯥꯛꯇꯕꯅ ꯂꯥꯛꯀꯅꯤ ꯍꯥꯌꯕ ꯇꯥꯀꯏ: ꯃꯤꯅꯤꯠ ꯀꯨꯟ ꯂꯥꯛꯇꯕ ꯕꯁ ꯑꯃꯥ ꯃꯊꯪꯒꯤ ꯃꯤꯅꯤꯠ ꯃꯉꯥꯗ ꯂꯥꯀꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯍꯦꯟꯅꯥ ꯂꯩ꯫ ꯃꯁꯤ ꯕꯁꯁꯤꯡ ꯃꯇꯃꯒꯤ ꯊꯥꯛꯇ ꯆꯠꯄꯅꯥ ꯑꯣꯏ꯫ ꯔꯨꯂꯦꯠꯇ ꯃꯇꯃꯒꯤ ꯊꯥꯛ ꯂꯩꯇꯦ; ꯃꯁꯤꯗ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯦꯊꯃꯦꯇꯤꯛꯁꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕꯃꯍꯩ ꯑꯃꯥ ꯊꯣꯛꯄꯒꯤ ꯈꯨꯗꯣꯡꯆꯥꯕ, 0 ꯗꯒꯤ 1 ꯐꯥꯑꯣꯕ ꯅꯠꯔꯒ 0% ꯗꯒꯤ 100% ꯐꯥꯑꯣꯕ꯫ ꯃꯁꯤꯡ ꯑꯃꯥ: 1/37 = 2.70%꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯂꯩ, ꯑꯃꯁꯨꯡ ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯥ ꯍꯥꯌꯕꯁꯤ ꯀꯣꯇꯥ ꯅꯠꯇꯦ꯫ ꯃꯤꯒꯤ ꯅꯨꯡꯁꯤꯠ ꯑꯁꯤ ꯃꯥꯂꯦꯃꯒꯤ ꯃꯌꯥꯃꯒꯤꯗꯃꯛ ꯆꯨꯝꯃꯤ ꯑꯃꯁꯨꯡ ꯆꯛꯔꯒꯤꯗꯃꯛ ꯑꯔꯥꯟꯕꯅꯤ꯫
ꯆꯥꯡ ꯌꯦꯡꯕ
ꯃꯍꯩ ꯕꯣꯔꯗꯁꯤꯡꯗꯒꯤ “ꯏꯪꯕ” ꯃꯁꯤꯡ ꯆꯥꯃꯥ ꯏꯊꯝ ꯊꯝꯗꯨꯅ ꯈꯨꯗꯤꯡꯃꯛ ꯃꯊꯪꯒꯤ ꯁ꯭ꯄꯤꯟ 37 ꯗ ꯕꯦꯠ ꯊꯝꯕꯤꯌꯨ꯫ ꯊꯣꯀꯄꯒꯤ ꯆꯥꯡ ꯑꯗꯨ ꯁ꯭ꯄꯤꯟ ꯑꯃꯗ 1/37 ꯑꯣꯏꯒꯅꯤ, ꯔꯦꯟꯗꯝ ꯑꯣꯏꯅ ꯈꯅꯈꯤꯕ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯒꯨꯝꯅ, ꯅꯣꯏꯖ ꯈꯔꯥ ꯍꯦꯟꯕ ꯍꯟꯊꯕ꯫ ꯃꯍꯩ ꯕꯣꯔꯗ ꯑꯁꯤ ꯃꯃꯥꯡꯒꯤ ꯋꯥꯐꯃꯁꯤꯡꯒꯤ ꯄꯥꯎꯅꯤ꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔ ꯑꯃꯒꯤꯗꯃꯛ ꯃꯁꯤꯗ ꯂꯥꯎꯊꯣꯀꯄꯒꯤ ꯀꯔꯤꯁꯨ ꯂꯩꯇꯦ, ꯑꯃꯁꯨꯡ ꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯆꯛꯔꯂꯦꯕꯕꯥꯏꯌꯥꯁ ꯂꯩꯕ ꯆꯛꯔꯁꯛꯇꯝꯒꯤ ꯑꯁꯣꯏꯕꯁꯤꯡꯅ ꯄꯣꯀꯦꯠ ꯈꯔꯕꯨ 1/37 ꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯊꯣꯛꯍꯟꯕ ꯆꯛꯔ꯫ ꯌꯥꯝꯅ ꯌꯥꯝꯗꯦ, ꯊꯝꯂꯕ ꯁ꯭ꯄꯤꯟ ꯂꯤꯁꯤꯡ ꯀꯌꯥꯅ ꯈꯛꯇꯃꯛ ꯈꯉꯕ ꯉꯝꯃꯤ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯗ (ꯃꯁꯤ ꯁꯣꯏꯗꯅ ꯈꯉꯅꯕꯒꯤꯗꯃꯛ ꯁ꯭ꯄꯤꯟ ꯂꯤꯁꯤꯡ ꯀꯌꯥ ꯃꯊꯧ ꯇꯥꯏ) ꯕꯦꯠ ꯊꯃꯒꯗꯕꯗꯤ ꯏꯪꯕꯁꯤꯡ ꯅꯠꯇꯅ ꯁꯥꯠꯄ ꯃꯁꯤꯡꯁꯤꯡꯑꯔꯥꯟꯕ ꯊꯥꯖꯕꯁꯥꯠꯄ ꯃꯁꯤꯡꯅꯛꯅꯗ ꯊꯥꯖꯈꯤꯕꯗꯒꯤ ꯍꯦꯟꯅꯥ ꯊꯣꯀꯈꯤꯕ ꯃꯁꯤꯡ꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔꯗ ꯃꯁꯤꯅ ꯀꯔꯤꯒꯨꯝꯕ ꯑꯃꯠꯇ ꯂꯥꯎꯊꯣꯛꯇꯦ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ →ꯅꯤ꯫
ꯑꯣꯟꯊꯣꯛꯂꯕ ꯑꯔꯥꯟꯕ ꯊꯥꯖꯕ
“ꯇꯔꯥꯇꯔꯦꯠ ꯁꯥꯠꯂꯤ, ꯃꯗꯨꯗ ꯕꯦꯠ ꯊꯝꯕꯤꯌꯨ” ꯍꯥꯌꯕꯁꯤ ꯁꯥꯏꯟ ꯑꯣꯟꯊꯣꯛꯂꯕ ꯑꯁꯣꯏꯕ ꯑꯗꯨꯃꯛꯅꯤ꯫ ꯊꯥꯖꯕ ꯑꯅꯤꯃꯛꯀꯤ ꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯦꯊꯃꯦꯇꯤꯛꯁꯐꯪꯒꯗꯕ ꯃꯃꯜꯃꯇꯝ ꯁꯥꯡꯅ ꯌꯦꯡꯂꯕꯗ ꯕꯦꯠ ꯑꯃꯒꯤ ꯑꯦꯚꯔꯦꯖ ꯃꯍꯩ꯫ ꯃꯔꯨꯑꯣꯏꯕ ꯌꯨꯔꯣꯄꯤꯌꯟ ꯕꯦꯠ ꯈꯨꯗꯤꯡꯗ ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −1/37꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯃꯤꯠ ꯃꯤꯠꯇꯨꯅ ꯈꯨꯠꯅ ꯇꯥꯛꯄꯒ ꯃꯥꯟꯅꯩ: ꯊꯝꯂꯕ ꯁꯦꯜꯒꯤ −2.70%꯫ ꯗꯦꯃꯣ ꯒꯦꯃꯗ ꯄꯨꯋꯥꯔꯤ ꯑꯗꯨ ꯆꯂꯥꯏꯗꯨꯅ ꯏꯪꯕ ꯃꯁꯤꯡꯑꯔꯥꯟꯕ ꯊꯥꯖꯕꯏꯪꯕ ꯃꯁꯤꯡꯁ꯭ꯄꯤꯟ ꯀꯌꯥꯒꯤ ꯃꯅꯨꯡꯗ ꯊꯣꯛꯇꯕ ꯃꯁꯤꯡ꯫ ꯆꯨꯝꯃꯤꯟꯅꯕ ꯆꯛꯔꯗ ꯃꯊꯪꯒꯤ ꯁ꯭ꯄꯤꯟꯁꯤꯡꯒꯤ ꯃꯇꯥꯡꯗ ꯀꯔꯤꯒꯨꯝꯕ ꯈꯉꯍꯟꯕ ꯑꯃꯠꯇ ꯄꯤꯗꯦ꯫ꯃꯄꯨꯡ ꯄꯥꯕꯤꯌꯨ → ꯑꯃꯥ ꯃꯊꯪꯒꯤ ꯁ꯭ꯄꯤꯟ 37 ꯗ ꯀꯌꯥ ꯌꯥꯝꯅ ꯊꯣꯀꯄꯒꯦ ꯃꯁꯤꯡ ꯊꯤꯕꯤꯌꯨ; ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨ ꯃꯇꯧ ꯀꯨꯞꯅ 63.7% ꯅꯤ, ꯑꯇꯣꯞꯄ ꯀꯔꯤꯒꯨꯝꯕ ꯃꯁꯤꯡ ꯑꯃꯒꯨꯝꯅ ꯆꯨꯃꯅ꯫
ꯋꯥꯍꯪꯁꯤꯡ
ꯁꯥꯟꯅꯔꯤꯕꯁꯤꯡꯅ ꯍꯪꯕꯅꯥ ꯎꯠꯂꯤ꯫ ꯕꯣꯔꯗ ꯑꯁꯤ ꯆꯨꯝꯃꯤ ꯑꯃꯁꯨꯡ ꯀꯥꯟꯅꯕ ꯂꯩꯇꯦ꯫
(36/37)⁵⁰⁰ ≈ 0.0001%: ꯈꯟꯅ ꯊꯣꯀꯏ, ꯑꯃꯁꯨꯡ ꯃꯊꯪꯒꯤ ꯁ꯭ꯄꯤꯟꯗ ꯍꯧꯖꯤꯛꯁꯨ 1/37꯫ ꯆꯛꯔ ꯑꯃꯗ ꯃꯁꯤ ꯃꯇꯝ ꯄꯨꯝꯕꯗ ꯊꯣꯛꯂꯕꯗꯤ, ꯃꯗꯨ ꯕꯥꯏꯌꯥꯁꯀꯤ ꯋꯥꯍꯪꯅꯤ, ꯑꯃꯁꯨꯡ ꯄꯥꯎꯈꯨꯝ ꯑꯗꯨꯗꯤ ꯃꯁꯤꯡ ꯑꯗꯨ ꯊꯥꯗꯣꯛꯀꯗꯕꯅꯤ꯫
ꯂꯥꯛꯂꯣꯏ꯫
ꯅꯣꯛꯅꯕꯒꯤ ꯀꯃꯤꯛ

ꯈꯨꯗꯣꯡꯆꯥꯕ ꯑꯃꯥ ꯍꯥꯌꯕꯁꯤ ꯀꯣꯇꯥ ꯅꯠꯇꯦ꯫
ꯍꯧꯔꯛꯐꯃꯁꯤꯡ
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.