Question

Quando P(A) = 1/2, P(B) = 2/3 e P(AUB) = 3/4, quanto vale
(a) P(A∩B)?
(b) P(Ac∩Bc)?

Answer 1

Resposta:

Explicação passo-a-passo:

P(A) = 1/2, P(B) = 2/3 e P(AUB) = 3/4.

a) P(AUB) = P(A) + P(B) - P(A∩B)

3/4 = 1/2 + 2/3 - P(A∩B)

P(A∩B) = 1/2 +2/3  - 3/4

P(A∩B) = (6+8 - 9)/12

P(A∩B) = 5/12

(b) Tem que aplicar a Lei de Morgan.

P(Ac∩Bc) =

P(AUB)^c =

1 - P(AUB) =

1 - 5/12 =

7/12