ᐊᐱᖅᑯᑎ: ᖃᖓᒃᑯᑦ ᓯᕉ ᓴᖅᑭᑦᑐᖅ
ᓯᕉ ᐊᔾᔨᒌᒃᑎᓪᓗᒋᑦ 37 ᑲᐃᕙᕐᓂᓂ ᐊᑕᐅᓯᐊᖅ ᓴᖅᑭᕙᒃᑐᖅ. ᓱᓕᓪᓚᕆᒃᑐᒥᒃ ᖃᓄᖅ ᐊᑯᓂᐅᑎᒋᔪᒥᒃ ᐅᑕᖅᑭᕙᖅᐱᑦ, ᖃᓄᐃᓕᐅᖅᐸᓪᓗ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ ᐱᙳᐊᖅᑎᒧᑦ?
ᓯᕉ ᐅᑕᖅᑭᓂᖅ geometric-ᖑᔪᖅ: ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ 37 ᑲᐃᕙᕐᓃᑦ, ᖃᑎᒃᑐᖅ 25, ᐅᑕᖅᑭᓃᓪᓗ ᒪᕐᕉᒃ ᖁᓕᑦ ᐃᓗᐊᓂ ᐊᑕᐅᓯᐊᖅ 110 ᑲᐃᕙᕐᓂᓂᑦ ᐊᑯᓂᐅᓂᖅᓴᐅᕙᒃᑐᖅ. 200 ᑲᐃᕙᕐᓂᓕᒻᒥ ᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ ᐱᙳᐊᖅᑎ 5.4 ᓯᕉᓂᒃ ᓂᕆᐅᒃᓴᖅᑐᖅ, ᑕᑯᔪᓐᓇᖅᑐᓗ 1-ᒥᑦ 10-ᒧᑦ.
ᐊᐱᖅᑯᑎ
ᓯᕉᐊᒃᓴᓗᐊᖅᓯᕉᐊᑕᐅᓯᖅ ᐅᔾᔪᐊᕌᔭᒃ ᐃᓂ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᖕᓄᑦ, ᑕᓴᓐᓄᑦ ᓇᑉᐸᖅᑐᓄᓪᓘᓐᓃᑦ ᐱᙳᐊᕈᑏᑦ ᐃᓚᐅᑎᙱᑕᖓ; ᑳᓯᓅᑉ ᐃᓚᖓᑕ ᐱᓇᓪᓗᑎᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐊᑕᐅᓯᖅ ᓯᕉ, 0.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑲᐃᕙᕐᓂᕐᒧᑦ 1/37-ᒥᒃ ᐱᔪᓐᓇᕐᓂᖃᖅᑐᖅᓈᓴᐃᓂᖅᐱᔪᓐᓇᕐᓂᖅᐱᓐᓂᐅᑉ ᐱᔪᓐᓇᕐᓂᖓ, 0-ᒥᑦ 1-ᒧᑦ ᐅᕝᕙᓘᓐᓃᑦ 0%-ᒥᑦ 100%-ᒧᑦ. ᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ: 1/37 = 2.70%.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ →. (a) ᑐᓪᓕᐊᓂ 37 ᑲᐃᕙᕐᓂᓂ ᓯᕉᖃᙱᓐᓂᕐᒧᑦ ᐱᔪᓐᓇᕐᓂᖅ ᖃᓄᐃᑦᑐᖅ? (b) ᖃᑎᒃᑐᖅ ᐅᑕᖅᑭᓂᖅ ᖃᓄᐃᑦᑐᖅ? (c) 200 ᑲᐃᕙᕐᓂᓕᒻᒥ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᖅᑕᐅᓂᖓᓂ, ᐱᙳᐊᖅᑎ ᓯᕉᓂᒃ ᖃᑦᓯᓂᒃ ᓂᕆᐅᒃᓴᖅᐸ, ᑭᒡᓕᖏᓪᓗ ᖃᓄᐃᑦᑑᕙ?
ᑭᐅᔾᔪᑏᑦ
(a) (36/37)³⁷ = 36.3%. ᐱᖓᓱᓂ ᐊᑕᐅᓯᐊᓂᑦ ᐊᒥᓲᓂᖅᓴᓂ, 37 ᑲᐃᕙᕐᓃᑦ ᓯᕉᖃᓐᖏᑦᑑᓪᓚᕆᑦᑐᑦ; ᑕᒪᓐᓇ ᐊᔾᔨᒋᔭᖓ ᓈᓴᐃᓂᖅ “37 ᑲᐃᕙᕐᓂᓂ ᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᐱᙳᐊᕈᑎᐊᑕᐅᓯᕐᒧᑦ ᐱᙳᐊᕈᑎᓈᓴᐅᑎ ᐊᑕᐅᓯᖅ, ᐊᑭᓕᐅᑎ 35:1.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐊᑕᐅᑦᑎᐊᖅ ᐅᖓᑖᓄᓪᓘᓐᓃᑦ ᓴᖅᑭᓂᐊᕐᓂᖓ” 63.7% ᑐᐊᖑᓂᖓᓂᒃ. (b) ᐅᑕᖅᑭᓂᖅ W geometric-ᖑᔪᖅ; p(W > k) = (36/37)ᵏ; ᖃᑎᒃᑐᖅ k-ᖑᔪᖅ ᑕᒪᓐᓇ 0.5-ᒥᒃ ᖃᖏᖅᑕᖓ, ᑕᒪᓐᓇ k ≈ 25. ᐅᑕᖅᑭᓃᑦ ᓇᑉᐸᖏᑦ 25 ᑲᐃᕙᕐᓃᑦ ᐅᕝᕙᓘᓐᓃᑦ ᓇᐃᓂᖅᓴᐅᔪᑦ, ᓇᑉᐸᖏᓪᓗ ᐊᑯᓂᐅᓂᖅᓴᐅᔪᑦ; ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ 37 ᐊᖏᓕᖅᑎᑕᐅᔪᖅ ᐊᑯᓂᐅᓗᐊᖅᑐᓄᑦ ᐅᑕᖅᑭᓂᕐᓄᑦ. (c) 200 ᑲᐃᕙᕐᓂᓂ ᓯᕉᑦ binomial-ᖑᔪᑦ, ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ 200/37 = 5.4, ᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓᓗᓈᓴᐃᓂᖅᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᐊᑦᔨᐅᑎᖓᐊᔾᔨᒌᙱᓐᓂᐅᑉ ᓯᑭᐊᖅᑐᓂᖓ (√); ᐱᓐᓂᐅᑉ ᓂᕆᐅᒋᔭᐅᔪᒥᑦ ᐊᑐᐃᓐᓇᐅᒐᔪᒃᑐᖅ ᐅᖓᓯᑦᑎᒋᓂᖓ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → √(200 × (1/37) × (36/37)) ≈ 2.3. 95% ᑭᒡᓕᖏᑦ ᖃᓂᒋᔭᖓ 1-ᒥᑦ 10-ᒧᑦ.
ᓯᕉ ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᓐᓄᑦ ᐱᙳᐊᖅᑎᒧᑦ ᖃᓄᖅ ᐊᑭᖃᕐᒪᖔᑦ
ᓯᕉ ᐊᑐᓂ ᐊᑕᐅᓯᕐᒥᒃ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᓂᒃ ᐊᑭᖃᖅᑐᖅ, ᓯᕉᓪᓗ ᐊᐅᐸᓗᒃᑐᒥᐱᙳᐊᕈᑎᐊᐅᐸᓗᒃᑐᖅᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ 18 ᐊᐅᐸᓗᒃᑐᓄᑦ ᓈᓴᐅᑎᓄᑦ. ᕖᓇᓯᑐᑦ: ᕈᔾ (rouge).ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᑳᓯᓅᑉ ᐃᓚᖓ ᐃᓘᓐᓇᖓ: 37 ᐊᔾᔨᒌᒃᑎᑕᐅᔪᓂ ᑲᐃᕙᕐᓂᓂ 18 ᐊᔪᒐᕐᓃᑦ 18-ᓪᓗ ᐊᓯᐅᔾᔨᓃᑦ ᐲᖅᓯᖃᑦᑕᖅᑐᑦ, ᓯᕉᓗ ᐊᑕᐅᓯᖅ −1/37-ᖑᔪᖅ. 200 ᑲᐃᕙᕐᓂᓕᒻᒥ ᐱᙳᐊᖅᑕᐅᓂᖓᓂ $10-ᒥᒃ, ᓂᕆᐅᒋᔭᐅᔪᑦ 5.4 ᓯᕉᑦ $54-ᒥᒃ ᐊᑭᖃᖅᑐᑦ, ᑕᒪᓐᓇ ᓱᓕᓪᓚᕆᒃᑐᒥᒃ 200 × $10 / 37. ᐱᙳᐊᖅᑕᐅᓂᖓ 2 ᓯᕉᓕᒃ $34-ᒥᒃ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᐅᔪᒥᒃ ᐱᓯᒪᔪᖅ; ᐱᙳᐊᖅᑕᐅᓂᖓ 9 ᓯᕉᓕᒃ $36-ᒥᒃ ᐱᔪᓐᓇᕐᓂᒃᑯᑦ ᐱᐅᙱᑦᑐᒥᒃ ᐱᓯᒪᔪᖅ, ᑕᒡᓚᖅᓯᒪᔪᑐᐊᓘᔮᕐᓂᐊᖅᑐᓗ. ᓚ ᐸᕐᑕᔾᒪᓕᒐᖅᓚ ᐸᕐᑕᔾᕖᓇᓯ ᒪᓕᒐᖓ: ᓯᕉ ᐊᔪᒐᖅᐸᑦ, ᐊᔾᔨᒌᒃᑐᒥᒃ ᐊᑭᓕᐅᑎᓕᒃ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ ᕿᑎᖓ ᐅᑎᖅᑎᑕᐅᔪᖅ. ᑕᐃᒃᑯᓂ ᐱᙳᐊᕈᑏᓐᓂ ᑳᓯᓅᑉ ᐃᓚᖓ ᕿᑎᐊᓄᑦ ᒥᑭᓕᒋᐊᖅᑎᑕᐅᔪᖅ, 1.35%-ᒧᑦ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐱᙳᐊᕐᕕᖓᓂ ᓯᕉ ᐊᑐᓂ ᐱᙳᐊᕈᑎ ᑮᓇᐅᔭᖓᑕ ᓇᑉᐸᖓᓂᒃ ᐊᑭᖃᖅᑐᖅ, ᓈᓴᐅᑏᓪᓗ ᓇᑉᐸᖏᓐᓄᑦ ᒥᑭᓕᖅᑐᑦ.
ᑐᓪᓕᐊ ᐊᐱᖅᑯᑎ
ᓯᕉᒃ ᒪᕐᕉᒃ ᑐᓪᓕᖅᑐᑦ ᓴᖅᑭᓂᐊᕐᓂᖏᓐᓄᑦ ᐱᔪᓐᓇᕐᓂᖅ ᖃᓄᐃᑦᑐᖅ? (1/37)² = 1/1,369. ᑳᓯᓄᒥ 20 ᐱᙳᐊᕐᕕᓕᒻᒥ, 50 ᑲᐃᕙᕐᓃᑦ ᐃᑲᕐᕋᒧᑦ, ᑕᒪᓐᓇ ᖃᓂᒋᔭᖓ ᓯᕉᒃ ᒪᕐᕉᒃ ᑐᓪᓕᖅᑐᑦ ᓇᐅᓕᒫᒃᑯᑦ 1.4 ᐃᑲᕐᕋᑦ ᐊᑐᓂ. ᐱᙳᐊᖅᑏᑦ ᑕᑯᔪᑦ ᐃᓱᒪᓕᐅᖅᑐᑦ ᐊᒃᓴᓗᐊᖅ ᓱᕋᒃᓯᒪᓂᖓᓂᒃ; ᓈᓴᐃᓂᐅᑉ ᐅᖃᐅᓯᖓ: ᐅᓪᓗᑐᐃᓐᓇᐅᔪᖅ.
ᐆᑦᑐᕐᓗᒍ
ᕉᓚᑦ: ᐱᙳᐊᖅᑕᐅᓂᖓᓂᒃ ᐊᔾᔨᐅᖅᑕᐅᑎ ᐱᙳᐊᖅᑕᐅᓂᖓᓂ ᐊᑐᓂ ᓯᕉᓂᒃ ᓈᓴᐃᔪᖅ. 100 ᑲᐃᕙᕐᓃᑦ ᐊᒥᓱᓂ ᕼᐊᓐᑐᕆᑦᓂ ᐱᒋᐊᕐᓗᒋᑦ, ᓈᓴᐅᑏᓪᓗ ᐊᑦᔨᓕᐅᕐᓗᒋᑦ: ᖁᓛᓂ ᐊᑦᔨᓕᐊᖅ ᓴᖅᑭᓂᐊᖅᑐᖅ, ᑕᓕᖅᐱᐊᓂ ᐊᑯᓂᐅᔪᒥᒃ ᐱᖃᓗᓂ. ᐅᓂᒃᑳᑦ ᑕᐃᑲᓂᑦ ᐱᓯᒪᔪᑦ.
ᓈᓴᐅᑎᓕᐅᕈᑎ
ᐊᐱᖅᑯᑏᑦ
ᓈᒻᒪᒃᑐᒥ ᐃᒪᐃᙱᑦᑐᖅ. ᓴᖑᓯᒪᔪᒥ ᐊᒃᓴᓗᐊᕐᒥᖃᐅᔨᓴᕐᕕᒃᓴᖑᓯᒪᔪᖅ ᐊᒃᓴᓗᐊᖅᐊᒃᓴᓗᐊᖅ ᓴᓇᓂᖓᑕ ᐊᑲᐅᙱᓐᓂᖏᑦ ᐃᓂᓂᒃ ᐃᓚᖏᓐᓂᒃ 1/37-ᒥᑦ ᐱᔪᓐᓇᕐᓂᖅᓴᐅᑎᑦᓯᔪᑦ. ᖃᐅᔨᔭᐅᑦᓯᐊᙱᑦᑐᖅ, ᑕᐅᓴᓐ ᐊᒥᓱᑦ ᑲᐃᕙᕐᓃᑦ ᑎᑎᕋᖅᑕᐅᓯᒪᒍᑎᒃ ᖃᐅᔨᔭᐅᔪᓐᓇᖅᑐᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᐃᓂᐊᑐᖅᑕᐅᔪᑦᐃᓂᑲᐃᕙᖅᑐᒥ 37 ᓈᓴᐅᑎᓕᑦ ᐃᓂᑦ ᐊᑕᐅᓯᖓ. ᐊᓯᐊᓂ ᐊᑎᖏᑦ: ᐃᓂᒋᐊᖅ, ᖃᓪᓗᐊᖅ.ᐃᓘᓐᓇᖓ ᐅᖃᓕᒫᕐᓗᒍ → ᓇᓪᓕᐊᑐᐃᓐᓇᖅ ᐃᒪᐃᔪᓐᓇᖅᑐᖅ, ᑕᐅᓴᓐᑦ ᑲᐃᕙᕐᓃᑦ ᐱᔭᕆᐊᖃᕐᓂᐊᖅᑐᑦ ᖃᐅᔨᓂᐊᖅᑎᓪᓗᒍ.
ᐱᙳᐊᕈᑎᐅᔪᖅ 2.70%-ᓕᒃ ᐊᓯᖏᑎᑐᑦ. ᐱᙳᐊᖅᑕᐅᓂᖓᑕ ᐱᐅᓯᖓᓂᒃ ᐊᓯᑦᑐᖅᓯᔪᖅ (ᓯᕉ ᐊᔪᒐᕐᓂᐅᓕᖅᑐᖅ), ᐊᑭᖓᓂᒃ ᐃᒪᐃᙱᑦᑐᖅ.
ᐅᑕᖅᑭᓃᑦ ᐊᕕᒃᓯᒪᓂᖏᑦ ᓴᖑᓯᒪᒻᒪᑕ: ᐊᒥᓱᑦ ᓇᐃᑦᑐᑦ ᐅᑕᖅᑭᓃᑦ, ᐊᒥᓲᙱᑦᑐᓪᓗ ᐊᑯᓂᐅᓪᓚᕆᒃᑐᑦ.
ᐃᓪᓗᕐᓇᖅᑐᖅ ᐊᔾᔨᓕᐊᖅ
ᐊᔾᔨᒌᒃᑎᑕᐅᔪᖅ 37, ᖃᑎᒃᑐᖅ 25, ᑕᓕᖅᐱᐊᓂᓗ ᐊᑯᓂᐅᔪᒥ ᐅᓂᒃᑳᑐᐊᑦ ᐃᓅᔪᑦ.
ᐱᕝᕕᒋᔭᐅᔪᑦ
- Feller, W. An Introduction to Probability Theory and Its Applications, Vol. 1.
- Ethier, S. N. The Doctrine of Chances: Probabilistic Aspects of Gambling.