Question

QUESTION 2 (0.5 POINTS) Let A and B be two events with P(AB) = 0.2, P(B) = 0.5, and P(A)=0.4, are A and B independent? Select the correct statement.

(a). Yes, A and B are independent because we could show that P(A)=P(A|B)
(b). No, A and B are not independent because we couldn’t show that P(A)=P(A|B)
(c). Yes, A and B are independent because we could show that P(AB)=P(A|B)
(d). We cannot tell if A and B are independent based on the information given

Answer 1

The correct option is (a) P (A|B) = P (A).

Explanation:

It is provided that:

P (A) = 0.40

P (B) = 0.50

P (A ∩ B) = 0.20

If events A and B are independent then:

`P(A|B)=P(A)`

Compute the value of P (A|B) as follows:

`P(A|B)=(P(A\cap B))/(P(B))=(0.20)/(0.50)= 0.40`

The value of P (A|B) = P (A).

Thus, the events A and B are independent.

The correct option is (a).