Question

IMPORTANT: I know the answer to the question is given below. However, I don't understand it. Please explain why A & B are independent when P(B)=1 and P(A)=0? Also, why are they not independent in all other cases?

State whether the following is True (T) or not always True (F) If A C B then A and B are not independent 6 ane net independant. (F) for ACB, e events A TP ACB hen Ae know As Cwe indenpent whan PCB) PCA)-o ie all other Casee A d 6 are not mdependout akoye 4 8 e geven Stalemeudt a not tocue, hance Paulse a

Answer 1

Given tha ACB A and B 92 und not mdepedent Given Statement s not Sol aloaye False thet Cwe bnoeD mdepasut Scid to be event PCANB) PCA) PIB) But Ure have AC B ANB A PCAJ PCANB) indepedlet preately So A anc ohen PCANB) PCAJ. PCB) PCA) if PCA)2O eyelity indlepelant +hey holds and So A qnc then T arc indepedout be So SE PCA) O 'n other case But KAJ PCB) cyuality PCA) = then the yefied would y cicelty PCAne) PCA). PCe) when So pCA) to Inelepsdlaut Cantt hol 'n al hot 9K A and B