Question

Select Independent or Not independent for each description of events.
P(A) = 0.6, P (B) = 0.5, P (AB) = 0.6
P(A)=0.8, P (B) = 0.2. P(AB) = 0.4
P(A) = 0.4, P (B) =0.3, P(AB) = 0.12​

Answer 1

Step-by-step explanation:

If A and B are independent, then P(A and B) = P(A) * P(B).

Then the probability that A occurs given that B occurs, for example, reduces to the probability that A occurs by itself:

P(A\mid B)=\dfrac{P(A\cap B)}{P(B)}=\dfrac{P(A)P(B)}{P(B)}=P(A)P(A∣B)=P(B)P(A∩B)=P(B)P(A)P(B)=P(A)

So all you need to do is check that P(A|B) = P(A). If so, then A and B are independent. This is true only for the second case.