Question

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) .

Answer 1

Explanation:

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

is the correct answer.

Answer 2

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

is the correct answer.

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.