| 1(A') | ||
Udowodnić że P(A|B)≥1− | ||
| P(B) |
| P(B)−P(A') | P(B∩A) | ||
= | = P(A/B) | ||
| P(B) | P(B) |
| P(A∩B | P(A) + P(B) − P(A∪B) | P(A) + P(B) − 1 | ||||
P(A|B) = | = | ≥ | = ... dokończ | |||
| P(B | P(B) | P(B) |
| P(B)−P(A') | P(A) | ||
≥1 − | |||
| PB | P(B) |
| P(B)−P(A') | P(B)−P(A) | ||
≥ | |||
| P(B) | P(B) |
| P(A)+P(B)−1 | P(A') | ||
≥1− | |||
| P(B) | P(B) |
| P(A)+P(B)−1 | P(B) | P(A') | |||
≥ | − | ||||
| P(B) | P(B) | P(B) |
| P(A)+P(B)−1 | P(B)−(1−P(A)) | ||
≥ | |||
| P(B) | P(B) |
| P(A)+P(B)−1 | P(B) +P(A)−1 | ||
≥ | |||
| P(B) | P(B) |
| P(A) + P(B) − 1 | P(B) | 1 − P(A) | P(A') | |||||
P(A|B) ... ≥ | = | − | = 1 − | |||||
| P(B) | P(B) | P(B) | P(B) |