Aand 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.