A and B are two events.

Let P (A) = 0.5, P (B) = 0.25, and P (A and B) = 0.15.

Which statement is true?

A and B are not independent events because P (A|B) ≠P (A).

A and B are not independent events because P (A|B) = P (A) and P (B|A) = P (B).

A and B are independent events because P (A|B) = P (B) and P (B|A) = P (A).

A and B are not independent events because P (A|B) = P (B) and P (B|A) = P (A).

A and B are not independent events because P (A|B) ≠P (A)

is the correct answer.

Step-by-step explanation:

If A and B are independent then we must have

P (AB) = P (A) P (B) and also

P (A/B) = P (A)

We are given that

A and B are two events.

Let P (A) = 0.5, P (B) = 0.25, and P (A and B) = 0.15.

P (A/B) = P (AB) / P (B) = 0.15/0.5 = 0.3

i. e. P (A/B) is not equal P (A)

Similarly P (B/A) = P (AB) / P (A) = 0.15/0.25 = 0.6 not equal to P (B)

Hence A and B are not independent.