The prior probabilities for events

A₁

and

A₂

are

P(A₁) =0.20

and

P(A₂) =0.80.

It is also known that

P(A₁A₂) = 0.

Suppose

P(B|A₁) =0.20

and

P(B|A₂) =0.10.

(a)Are

A₁

and

A₂

mutually exclusive?They ---Select--- are are not mutually exclusive.How could you tell whether or not they are mutually exclusive?

P(A₂)P(A₂|A₁)P(A₁A₂) = 0 P(A₁)P(A₁|A₂)P(A₁) +P(A₂) = 1P(B|A₁)P(B|A₂)

(b)Compute

P(A₁B)

and

P(A₂B).

P(A₁B)

=

P(A₂B)

= (c)Compute

P(B).

(d)Apply Bayes' theorem to compute

P(A₁|B)

and

P(A₂|B).

(Round your answers to four decimal places.)

P(A₁|B)

=

P(A₂|B)

=