Question

In: Statistics and Probability

The prior probabilities for events A1 and A2 are P(A1) = 0.50 and P(A2) = 0.45....

The prior probabilities for events A₁ and A₂ are P(A₁) = 0.50 and P(A₂) = 0.45. 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 A₁ and A₂ mutually exclusive?

- Select your answer -YesNoItem 1

Explain your answer.

The input in the box below will not be graded, but may be reviewed and considered by your instructor.

(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) =

Expert Solution

a) We know two events are mutually exclusive or disjoint if they cannot both occur at the same time ,

Since

Thus are mutually exclusive

b) Using Definition of conditional Probability we have

c) NOTE- Its not possible to find P(B) with the given condition.

In order to find P(B) we have to assume that are mutually exclusive as well as Exhaustive, which is possible when

Then using Total Probability theorem we get

d) NOTE- Its not possible to Apply Bayes theorem, as the theorem requires to be mutually exclusive as well as Exhaustive, which is possible when .

If we change then

orchestra answered 2 years ago

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