P赤赤 = | 3 5 |
× | 2 4 |
= | 3 10 |
P赤白 = | 3 5 |
× | 2 4 |
= | 3 10 |
P白赤 = | 2 5 |
× | 3 4 |
= | 3 10 |
P白白 = | 2 5 |
× | 1 4 |
= | 1 10 |
|
H(A, B) = | 3 10 |
log2 | 10 3 |
+ | 3 10 |
log2 | 10 3 |
+ | 3 10 |
log2 | 10 3 |
+ | 1 10 |
log2 | 10 1 |
= | 9 10 |
log2 | 10 3 |
+ | 1 10 |
log2 | 10 1 | ||||||||
≒ 1.8955 (bit) |
H(A) = | 3 5 |
log2 | 5 3 |
+ | 2 5 |
log2 | 5 2 |
≒ 0.9710 (bit) |
H(B) = | 3 5 |
log2 | 5 3 |
+ | 2 5 |
log2 | 5 2 |
≒ 0.9710 (bit) |
H(A) + H(B) ≒ 1.9420 (bit) > H(A, B) |
H(B|A赤) = | P(B赤|A赤) | log2 | 1 P(B赤|A赤) |
+ | P(B白|A赤) | log2 | 1 P(B白|A赤) |
= | 2 4 |
log2 | 4 2 |
+ | 2 4 |
log2 | 4 2 |
= 1 (bit) |
H(B|A白) = | P(B赤|A白) | log2 | 1 P(B赤|A白) |
+ | P(B白|A白) | log2 | 1 P(B白|A白) |
= | 3 4 |
log2 | 4 3 |
+ | 1 4 |
log2 | 4 1 |
= | 2 - | 3 4 |
log2 | 3 (bit) |
H(B|A) = | P(A赤)H(B|A赤) + P(A白)H(B|A白) |
= | 3 5 |
× 1 + | 2 5 |
× ( | 2 - | 3 4 |
log2 | 3 | ) |
= | 7 5 |
- | 3 10 |
log2 | 3 | ≒ 0.9245 (bit) |