[前スレ.994]

[前スレ.999] の続き

P(3|T) = P(j+k≡0)
　= Σ[L=0，3n] Ｃ[3n，L] (2/3)^L (1/3)^(3n-L) {1+ω^L + ω^(-L)}/3
　= {1 + ((1+2ω)/3)^(3n) + ((1+2/ω)/3)^(3n)}/3
　= {1 + (1/3)^(3n/2)[i^(3n) + (-i)^(3n)]}/3
　= {1 + (1/3)^(3n/2)[(-i^)^n + i^n]}/3
　= {1 + (1/3)^(3n/2)･2cos(nπ/2)}/3,

P(3|T ∧ 3|S) = P(j≡0 ∧ k≡0)
　= Σ[0≦j+k≦3n] (3n)!/{j! k! (3n-j-k)!} (1/3)^(3n) {1+ω^j +ω^(-j)}/3・{1+ω^k +ω^(-k)}/3
　= {1 + ((1+2ω)/3)^(3n) + ((1+2/ω)/3)^(3n) + 2((2+ω)/3)^(3n) + 2((2+1/ω)/3)^(3n) + 0^(3n)}/9
　= {1 + (1/3)^(3n/2)[i^(3n) + (-i)^(3n) + 2((√3 +i)/2)^(3n) + 2((√3 -i)/2)^(3n)]}/9
　= {1 + (1/3)^(3n/2)[(-i)^n + i^n + 2･i^n + 2(-i)^n]}/9
　= {1 + (1/3)^(3n/2)･6cos(nπ/2)}/9,

P(3|T ∧ 3|S) / P(3|T)
　= {1 + 4cos(nπ/2)/[3^(3n/2) +2cos(nπ/2)]}/3,
かな