Question

Sendo p(a) = 1/2 e p ( a U b) = 3/4 obtenha p (b) nos sequintes casos a e b sao independente e a e b são desjuntos

Answer 1

Resposta:

Explicação passo-a-passo:

Se A e B são independentes, então P(A∩B) = P(A).P(B).

P(AUB)= P(A) + P(B) - P(A∩B)

P(AUB)= P(A) + P(B) - P(A).P(B) =

3/4 = 1/2 + (1/2).P(B)

3/4 = 1/2 + [P(B)]/2

3/4 - 1/2 = [P(B)]/2

3/4 - 2/4 = [P(B)]/2

1/4 = [P(B)]/2

4P(B) = 2

P(B) = 2/4

P(B) = 1/2

==//==

Se A e B são disjuntos​, então A∩B = ∅. Logo P(A∩B) = 0

P(AUB)= P(A) + P(B) - P(A∩B)

3/4= 1/2 + P(B) - 0

3/4- 1/2 = P(B)

P(B) = 1/4