| 2 | 3 | 1 | ||||
O zdarzeniach A, B ⊂ Ω wiadomo, że P(A') ≥ | , P(B) = | oraz P(A ∩ B) ≥ | . | |||
| 3 | 8 | 8 |
| 1 | ||
a) P(A − B) < | ||
| 4 |
| 7 | ||
b) P(A ∪ B) ≤ | . | |
| 12 |
| 2 | ||
P(A') ≥ | i P(A')=1−P(A) | |
| 3 |
| 2 | 1 | 1 | ||||
1−P(A)≥ | ⇒ P(A)≤ | i −P(A∩B)≤− | ||||
| 3 | 3 | 8 |
| 1 | 1 | 5 | 6 | 1 | ||||||
zatem P(A−B) ≤ | − | = | < | = | ||||||
| 3 | 8 | 24 | 24 | 4 |
| 1 | ||
P(A−B)< | ||
| 4 |
| 1 | ||
P(A)≤ | ||
| 3 |
| 3 | ||
P(B)= | ||
| 8 |
| 1 | ||
−P(A∩B)≤ − | ||
| 8 |
| 1 | 3 | 1 | 1 | 1 | 7 | |||||||
P(A)+P(B)−P(A∩B)= P(AUB) ≤ | + | − | = | − | = | |||||||
| 3 | 8 | 8 | 3 | 4 | 12 |
| 7 | ||
P(AUB) ≤ | ||
| 12 |