- Mathematical sets
- P(A∪B) = p(A) + P(B) - P(A∩B)
- P(A)' = 1 - P(A)
- P(Ω) = 1
- P(Ω)' = 0
- P(A∩B) = P(A) ⋅ P(B)
- P(A∩B) = [∀x∈A → x∈B
- P(A∩Ω) = P(A)
- P(A∪∅) = P(A)
- P(A∩∅) = ∅
- P(A'∪ Ω') = P(A')
- P(A|B) = P(A∩B) / P(B)
Probability of A given that B has already occurred
From img:
we have 10000 (100%) persons
With Disease 200 (2%) = P(D)
- positive 180 (90%) = P(P|D)
- negative 20 (10%) = P(P'|D)
With no Disease 9800 (98%) = P(D')
- positive 980 (10%) = P(P|D')
- negative 8820 (90%) = P(P'|D')
Dado que B sucede la probabilidad de que A suceda
De la Imagen:
Tenemos 10000 (100%) personas
Enfermas 200 (2%) = P(D)
- positivo 180 (90%) = P(P|D)
- negativo 20 (10%) = P(P'|D)
No enfermas 9800 (98%) = P(D')
- positivo 980 (10%) = P(P|D')
- negativo 8820 (90%) = P(P'|D')
| P | P' | ||
|---|---|---|---|
| D | 180 | 20 | 200 |
| D' | 980 | 8820 | 9800 |
| 1160 | 8840 | 10000 |
- P(P) = 8840 / 10000 = 0.884
- P(P') = 1160 / 10000 = 0.116
- P(D|P) = 180 / 1160 = 0.1551
- P(D'|P) = 980 / 1160 = 0.8448
- P(D|P') = 20 / 8840 = 0.0022
- P(D'|P') = 8820 / 8840 = 0.9977