The prior probabilities for events A₁and A₂are P(A₁) = 0.35 and P(A₂) = 0.65. It is also known that P(A₁ A₂) = 0. Suppose P(B | A₁) = 0.20 and P(B | A₂) = 0.05. If needed, round your answers to three decimal digits.

(a)

Are A₁and A₂mutually exclusive?

Answer.

(b)

Compute P(A₁ B) and P(A₂ B).

P(A1 B) =
P(A2 B) =

(c)

Compute P(B).

P(B) =

(d)

Apply Bayes' theorem to compute P(A₁| B) and P(A₂| B).

P(A1| B) =
P(A2| B) =